عرض مصدر قائمة الثوابت الرياضية

[[ثابت رياضي|الثابت الرياضي]] هو [[رقم]]، له دلالة خاصة في العمليات الحسابية. على سبيل المثال، الثابت الرياضي [[ط (رياضيات)|باي]] (''π'') يعني نسبة طول [[محيط منحنى مغلق|محيط الدائرة]] إلى [[قطر (هندسة)|قطرها]]. هذه القيمة ثابته لا تتغير لأي [[دائرة]].

== بيانات الجدول ==
* [[قيمة (رياضيات)|القيمة العددية]] للثابت: من المراجع العالمية ك[[موقع ماثوورلد]] أو من [[موسوعة المتتاليات الصحيحة على الإنترنت]] والتي تعرف اختصارا باسم [http://oeis.org/wiki/Main_Page أويس ويكي (OEIS)].
* [[لاتخ]]: الصيغة في تنسيق [[تخ (برمجية)|تخ]].
* [[صيغة رياضية|الصيغة الرياضية]]: المستخدمة في برنامج [[ولفرام ألفا]].
* [[موسوعة المتتاليات الصحيحة على الإنترنت|أويس]]: موسوعة على الإنترنت عن الأعداد الصحيحة.
* [[كسر مستمر|الكسر المستمر]]: وهو الكسر الذي يأخذ الصيغة التالية
:<math>x = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + \cfrac{1}{\ddots\,}}}} </math>
* العام: عام اكتشاف الثابت.
* تنسيق الويب: القيمة بشكل مناسب على صفحات الإنترنت.
* النوع: نوع العدد.
** ك: [[عدد كسري]]
** غ.ك: [[عدد غير كسري|عدد غير نسبي]] (عدد غير كسري)
** ج : [[عدد جبري]]
** م : [[عدد متسام]]
** خ : [[عدد مركب]]
== جدول الدوال والثوابت الرياضية ==
هذا الجدول يهتم بأهم '''الدوال والثوابت الرياضية''' على مر العصور:

{| class="wikitable sortable"
|-
! القيمة العددية||  الاسم||الرسومات||الرمز|| لاتخ||  الصيغة||النوع|| أويس ويكي|| الكسر المستمر||العام||تنسيق الويب
|-

<!-----------------------------------------v----------------------------------------->
|0.74048048969306104116 
||ثابت هيرميت [[تعبئة الكرات]] بنظام ثلاثي الأبعاد [[حدسية كيبلر]] <ref>{{استشهاد بكتاب
|مؤلف1=Thomas Hales |مؤلف2=Samuel Ferguson |سنة= 2010
|عنوان= The Kepler Conjecture: The Hales-Ferguson Proof
|ناشر= Springer
|محرر=Jeffrey C. Lagarias
|مسار= https://books.google.com/?id=qKNAHyQQcssC&lpg=PR4&pg=PR4#v=onepage&q&f=false
|isbn= 978-1-4614-1128-4
|مسار أرشيف= https://web.archive.org/web/20200304172839/https://books.google.com/?id=qKNAHyQQcssC&lpg=PR4&pg=PR4#v=onepage&q&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Pyramid of 35 spheres animation large.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\mu_{_{K}}} </math> 
||<math>\frac{\pi}{3\sqrt{2}} {\color{white}......\color{black}} </math> أثبت توماس هيلز في عام 2014 أن حدثية كيبلر صحيحة.<ref>{{استشهاد بكتاب
|مؤلف= Thomas C. Hales
|سنة= 2014
|عنوان= Introduction to the Flyspeck Project
|ناشر=Math Department, University of Pittsburgh
|مسار= https://drops.dagstuhl.de/opus/volltexte/2006/432/pdf/05021.HalesThomas.Paper.432.pdf
| مسار أرشيف = https://web.archive.org/web/20180515142135/http://drops.dagstuhl.de/opus/volltexte/2006/432/pdf/05021.HalesThomas.Paper.432.pdf | تاريخ أرشيف = 15 مايو 2018 }}</ref> 
||<syntaxhighlight lang="mathematica">
 pi/(3 sqrt(2))
 </syntaxhighlight>
||
||{{OEIS2C|A093825}}
||[0;1,2,1,5,1,4,2,2,1,1,2,2,2,6,1,1,1,5,2,1,1,1, ...]
||1611
||<small> 0.74048048969306104116931349834344894 </small>
|-

<!---------------------------------------------v---------------------------------------->
|22.45915771836104547342
||pi^e <ref>{{استشهاد بكتاب
|مؤلف= John Derbyshire
|عنوان= Prime Obsession: Bernhard Riemann and the Greatest unsolved problem
|صفحة=319
|سنة= 2003
|ناشر= Joseph Henry Press
|isbn= 0-309-08549-7
|مسار= https://books.google.com/?id=qsoqLNQUIJMC&pg=PA319&dq=22.45915771836#v=onepage&q=22.45915771836&f=false
|مسار أرشيف= https://web.archive.org/web/20200304172841/https://books.google.com/?id=qsoqLNQUIJMC&pg=PA319&dq=22.45915771836#v=onepage&q=22.45915771836&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br />
| bgcolor=#e0f0f0 align=center|<math>\pi^{e} </math>
||<math>\pi^{e} </math>
||<syntaxhighlight lang="mathematica">
 pi^e
 </syntaxhighlight>
||
||{{OEIS2C|A059850}}
||[22;2,5,1,1,1,1,1,3,2,1,1,3,9,15,25,1,1,5,...]
||
||<small> 22.4591577183610454734271522045437350 </small>
|-

<!----------------------------------------v------------------------------------------->
|2.80777024202851936522 
||ثابت فرانسين روبنسون <ref>{{استشهاد بكتاب
|مؤلف= Dusko Letic, Nenad Cakic, Branko Davidovic and Ivana Berkovic
|عنوان= Orthogonal and diagonal dimension fluxes of hyperspherical function
|مسار= https://advancesindifferenceequations.springeropen.com/track/pdf/10.1186/1687-1847-2012-22.pdf
|ناشر= Springer
| مسار أرشيف = https://web.archive.org/web/20140808053154/http://www.advancesindifferenceequations.com/content/pdf/1687-1847-2012-22.pdf | تاريخ أرشيف = 8 أغسطس 2014 }}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{F}</math>
||<math>\int_{0}^\infty \frac{1}{\Gamma(x)}\, dx. = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, dx</math>
||<syntaxhighlight lang="mathematica">
N[int[0 to ∞] {1/Gamma(x)}]
 </syntaxhighlight>
||
||{{OEIS2C|A058655}}
||[2;1,4,4,1,18,5,1,3,4,1,5,3,6,1,1,1,5,1,1,1...]
||1978
||<small> 2.80777024202851936522150118655777293 </small>
|-

<!--------------------------------------v--------------------------------------------->
|1.305686729 ≈ بواسطة توماس ودهار <br />1.305688 ≈ بواسطة ماكمولين 
||[[كسيرة|الهندسة الكسيرية]] ل[[أبلونيوس البرغاوي]] <br /> <ref>{{استشهاد بكتاب 
|مؤلف= Benoit Mandelbrot
|عنوان= Fractals and Chaos: The Mandelbrot Set and Beyond
|مسار= https://books.google.com/?id=q0AmBQAAQBAJ&lpg=PA184&dq=1.305686729&pg=PA184#v=onepage&q=1.305686729&f=false
|سنة= 2004
|isbn= 978-1-4419-1897-0
|مسار أرشيف= https://web.archive.org/web/20200304172843/https://books.google.com/?id=q0AmBQAAQBAJ&lpg=PA184&dq=1.305686729&pg=PA184#v=onepage&q=1.305686729&f=false|تاريخ أرشيف=2020-03-04}}</ref> {{,}} <ref>{{استشهاد بكتاب 
|مؤلف= Curtis T. McMullen
|عنوان= Hausdorff dimension and conformal dynamics III: Computation of dimension
|مسار= http://abel.math.harvard.edu/~ctm/papers/home/text/papers/dimIII/dimIII.pdf
|سنة= 1997
| مسار أرشيف = https://web.archive.org/web/20170809045213/http://abel.math.harvard.edu/~ctm/papers/home/text/papers/dimIII/dimIII.pdf | تاريخ أرشيف = 9 أغسطس 2017 }}</ref> 
||[[ملف:ApollonianGasket-15 32 32 33.svg|100px]]
| bgcolor=#e0f0f0 align=center|<br /><math>\varepsilon</math>
||
||
||
||{{OEIS2C|A052483}}
||[0;3,2,3,16,8,10,3,1,1,2,1,3,1,2,13,1,1,4,1,5,...]
||1994 <br /> 1998
||1.305686729 ≈ <br /> 1.305688 ≈
|-

<!-------------------------------------------v------------------------------------------>
|0.43828293672703211162 <br />
0.360592471871385485 [[وحدة تخيلية|i]] 
||[[رفع (رياضيات)|الأس]] الانهائي [[وحدة تخيلية|للوحدة التخليلة]]''[[وحدة تخيلية|i]]'' <ref>{{استشهاد بكتاب 
|عنوان= Properties of the Lambert Function W(z) 
|مسار= http://www2.mae.ufl.edu/~uhk/LAMBERT3.pdf 
| مسار أرشيف = https://web.archive.org/web/20160303234059/http://www2.mae.ufl.edu/~uhk/LAMBERT3.pdf | تاريخ أرشيف = 3 مارس 2016 }}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math> {}^\infty {i} </math>
||<math> \lim_{n \to \infty}  {}^n i  =  \lim_{n \to \infty}  \underbrace{i^{i^{\cdot^{\cdot^{i}}}}}_n  </math>
||<syntaxhighlight lang="mathematica">
 i^i^i^i^i^i^...
 </syntaxhighlight>
|'''[[عدد مركب|خ]]'''
||{{OEIS2C|A077589}} <br /> {{OEIS2C|A077590}}
||[0;2,3,1,1,4,2,2,1,10,2,1,3,1,8,2,1,2,1, ...] <br /> + [0;2,1,3,2,2,3,1,5,5,1,2,1,10,10,6,1,1...] ''i''
||
||<small> 0.43828293672703211162697516355126482 <br /> + 0.36059247187138548595294052690600 ''i'' </small>
|-
<!-----------------------------------------v------------------------------------------->
|0.9288358271 
||مجموع مقلوب [[عددان أوليان توأم|الأعداد الأولية التوأم]] 
||
|bgcolor=#e0f0f0 align=center|<math>B_1</math>
||<math>\frac{1}{4}+\frac{1}{6}+\frac{1}{12}+\frac{1}{18}+\frac{1}{30}+\frac{1}{42}+\frac{1}{60}+\frac{1}{72}+\cdots</math>
||<syntaxhighlight lang="mathematica">
1/4 + 1/6 + 1/12 + 1/18 + 1/30 + 1/42 + 1/60 + 1/72 + ...
 </syntaxhighlight>
||
|{{OEIS2C|A241560}}
||[0; 1, 13, 19, 4, 2, 3, 1, 1]
||2014
||0.928835827131
|-

<!---------------------------------------------v--------------------------------------->
|0.63092975357145743709 
||[[مجموعة كانتور]] <ref>{{استشهاد بكتاب
|مؤلف= Paul Manneville
|عنوان= Instabilities, Chaos and Turbulence
|صفحة= 176
|سنة= 2010
|ناشر= Imperial College Press
|isbn= 978-1-84816-392-8
|مسار= https://books.google.com/?id=6-GivG81u6oC&lpg=PA176&dq=0.63092975&pg=PA176#v=onepage&q=0.63092975&f=false
|مسار أرشيف= https://web.archive.org/web/20200304172845/https://books.google.com/?id=6-GivG81u6oC&lpg=PA176&dq=0.63092975&pg=PA176#v=onepage&q=0.63092975&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Cantor5.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>d_f(k)</math>
||<math> \lim_{\varepsilon \to 0} \frac {\log N(\varepsilon)}{\log (1/\varepsilon)} = \frac{\log 2}{\log 3} </math>
||<syntaxhighlight lang="mathematica">
log(2)/log(3) 
 N[3^x=2]
 </syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A102525}}
||[0;1,1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...]
||
||<small> 0.63092975357145743709952711434276085 </small>
|-

<!------------------------------------------v------------------------------------------>
|0.31830988618379067153
|| مقلوب [[ط (رياضيات)|باي]] (π), [[سرينفاسا أينجار رامانجن]]<ref>{{استشهاد بكتاب
|مؤلف1=J.L. Berggren |مؤلف2=Jonathan M. Borwein |مؤلف3=Peter Borwein |عنوان= Pi: A Source Book
|سنة= 2003
|صفحة= 637
|ناشر= Springer-Verlag
|isbn= 0-387-20571-3
|مسار= https://books.google.com/?id=QlbzjN_5pDoC&lpg=PA637&dq=%22Ramanujan's%20sum.%20This%20amazing%20%22&pg=PA637#v=onepage&q=%22Ramanujan's%20sum.%20This%20amazing%20%22&f=false|مسار أرشيف= https://web.archive.org/web/20200304172847/https://books.google.com/?id=QlbzjN_5pDoC&lpg=PA637&dq=%22Ramanujan's%20sum.%20This%20amazing%20%22&pg=PA637#v=onepage&q=%22Ramanujan's%20sum.%20This%20amazing%20%22&f=false|تاريخ أرشيف=2020-03-04}}</ref> 
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>\frac{1}{\pi}</math>
||<math> \frac{2\sqrt{2}}{9801} \sum^\infty_{n=0} \frac{(4n)!\,(1103+26390 \; n)}{(n!)^4 \, 396^{4n}}</math>
||<syntaxhighlight lang="mathematica"> 2 sqrt(2)/9801 
 * Sum[n=0 to ∞] 
 {((4n)!/n!^4)
  *(1103+ 26390n)
  / 396^(4n)} </syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A049541}}
||[0;3,7,15,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,...]
||
||<small> 0.31830988618379067153776752674502872 </small>
|-

<!-------------------------------------------v----------------------------------------->
|0.28878809508660242127
||فلاجوليت وريتشموند <ref>{{استشهاد بكتاب 
|مؤلف1=Michael Jacobson |مؤلف2=Hugh Williams |عنوان= Solving the Pell Equation
|مسار= https://books.google.com/?id=2INzqrEUGzAC&lpg=PA159&dq=0.288788095&pg=PA159#v=onepage&q=0.288788095&f=false
|سنة= 2009
|ناشر= Springer
|isbn= 978-0-387-84922-5
|صفحة= 159
|مسار أرشيف= https://web.archive.org/web/20200304172849/https://books.google.com/?id=2INzqrEUGzAC&lpg=PA159&dq=0.288788095&pg=PA159#v=onepage&q=0.288788095&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{Q}</math>
||<math> \prod_{n=1}^{\infty} \left(1 - \frac{1}{2^n}\right) = \left(1{-}\frac{1}{2^1}\right) \left(1{-}\frac{1}{2^2} \right)\left(1{-}\frac{1}{2^3} \right) ... </math>
||<syntaxhighlight lang="mathematica"> prod[n=1 to ∞]
{1-1/2^n} </syntaxhighlight>
||
||{{OEIS2C|A048651}}
||[0;3,2,6,4,1,2,1,9,2,1,2,3,2,3,5,1,2,1,1,6,1,...]
||1992
||<small> 0.28878809508660242127889972192923078 </small>
|-

<!--------------------------------------------v--------------------------------------->
|1.53960071783900203869
||ثابت إليوت هرشل ليب للجليد (يستخدم في تحديد عدد [[دارة أويلرية|المسارات الاويلرية]]) <ref>{{استشهاد بكتاب
|مؤلف= Robin Whitty
|عنوان= Lieb’s Square Ice Theorem
|مسار= http://www.theoremoftheday.org/MathPhysics/Lieb/TotDLieb.pdf
| مسار أرشيف = https://web.archive.org/web/20190127035258/https://www.theoremoftheday.org/MathPhysics/Lieb/TotDLieb.pdf | تاريخ أرشيف = 27 يناير 2019 }}</ref>
||[[ملف:Sixvertex2.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{W}_{2D}</math>
||<math>\lim_{n\to\infty}(f(n))^{n^{-2}}=\left(\frac{4}{3}\right)^\frac{3}{2}=\frac{8}{3\sqrt3}</math>
||<syntaxhighlight lang="mathematica"> (4/3)^(3/2) </syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A118273}}
||[1;1,1,5,1,4,2,1,6,1,6,1,2,4,1,5,1,1,2,...]
||1967
||<small> 1.53960071783900203869106341467188655 </small>
|-

<!------------------------------------------v------------------------------------------>
|0.20787957635076190854 
||<math>i^i</math> <ref>{{استشهاد بكتاب
|مؤلف= Reinhold Remmert
|عنوان= Theory of Complex Functions
|مسار= https://books.google.com/?id=uP8SF4jf7GEC&lpg=PA162&dq=0.2078795763&pg=PA162#v=onepage&q=0.2078795763&f=false|سنة= 1991
|ناشر= Springer
|isbn= 0-387-97195-5
|صفحة= 162
|مسار أرشيف= https://web.archive.org/web/20200304172851/https://books.google.com/?id=uP8SF4jf7GEC&lpg=PA162&dq=0.2078795763&pg=PA162#v=onepage&q=0.2078795763&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br />
| bgcolor=#e0f0f0 align=center|<math>i^i</math>
|| <math>e^{-\frac{\pi}{2}}</math>
||<syntaxhighlight lang="mathematica"> e^(-π/2) </syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A049006}}
||[0;4,1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,...]
||1746
||<small> 0.20787957635076190854695561983497877 </small>
|-

<!-----------------------------------------v------------------------------------------->
|4.53236014182719380962
||ثابت فان دير باو
||
| bgcolor=#e0f0f0 align=center|<math> {\alpha} </math>
|| <math>\frac{\pi}{\ln(2)}=\frac{\sum\limits_{n=0}^\infty \frac{4(-1)^n}{2n+1}}{\sum\limits_{n=1}^\infty \frac{(-1)^{n+1}}{n}}=\frac{\frac{4}{1}-\frac{4}{3}+\frac{4}{5}-\frac{4}{7}+\frac{4}{9}-\cdots}{\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\cdots}</math>
||<syntaxhighlight lang="mathematica"> π/ln(2) </syntaxhighlight>
||
||{{OEIS2C|A163973}}
||[4;1,1,7,4,2,3,3,1,4,1,1,4,7,2,3,3,12,2,1,...]
||
||<small> 4.53236014182719380962768294571666681 </small>
|-

<!------------------------------------------v----------------------------------------->
|0.76159415595576488811 
||[[دوال زائدية|دالة زائدية]] للعدد 1 <ref>{{استشهاد بأرخايف
|مؤلف= Marek Wolf
|عنوان= Continued fractions constructed from prime numbers
|سنة= 2010
|arxiv= 1003.4015
|class=math.NT}}</ref>
||[[ملف:Hyperbolic Tangent.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>{th} \, 1</math>
||<math>-i \tan (i) = \frac{e-\frac{1}{e}}{e+\frac{1}{e}} = \frac{e^2-1}{e^2+1}</math>
||<syntaxhighlight lang="mathematica"> (e-1/e)/(e+1/e) </syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A073744}}
||[0;1,3,5,7,9,11,13,15,17,19,21,23,25,27,...] <br /> = [0;{{سطر فوقي|2p+1}}], p∈ℕ
||
||<small> 0.76159415595576488811945828260479359 </small>
|-

<!------------------------------------------v----------------------------------------->
|0.59017029950804811302 
||ثابت تشيبيشيف <ref>{{استشهاد بكتاب
|مؤلف= Steven Finch
|عنوان= Electrical Capacitance
|صفحة= 1
|سنة= 2014
|ناشر= Harvard.edu
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/capa.pdf
| مسار أرشيف = https://web.archive.org/web/20160419150944/http://www.people.fas.harvard.edu/~sfinch/csolve/capa.pdf | تاريخ أرشيف = 19 أبريل 2016 }}</ref>{{,}}<ref>{{استشهاد بكتاب 
|مؤلف= Thomas Ransford
|عنوان= Computation of Logarithmic Capacity
|صفحة= 557
|مسار= https://www.heldermann-verlag.de/cmf/cmf10/cmf10029.pdf
|ناشر= Université Laval, Quebec (QC), Canada
|مسار أرشيف= https://web.archive.org/web/20200414182752/http://www.heldermann-verlag.de/cmf/cmf10/cmf10029.pdf|تاريخ أرشيف=2020-04-14}}</ref>
||<br /><br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{\lambda_{Ch}}</math>
||<math>\frac{\Gamma(\tfrac14)^2}{4 \pi^{3/2}} = \frac{4 (\tfrac14 !)^2}{\pi^{3/2}}</math>
||<syntaxhighlight lang="mathematica">(Gamma(1/4)^2)
/(4 pi^(3/2))</syntaxhighlight>
||
||{{OEIS2C|A249205}}
||[0;1,1,2,3,1,2,41,1,6,5,124,5,2,2,1,1,6,1,2,...]
||
||<small> 0.59017029950804811302266897027924429 </small>
|-

<!----------------------------------------v---------------------------------------->
|0.07077603931152880353 <br />
0.6840003894379-
||MKB ثابت <br /><ref>{{استشهاد بأرخايف
|مؤلف= RICHARD J. MATHAR
|عنوان= NUMERICAL EVALUATION OF THE OSCILLATORY INTEGRAL BETWEEN 1 AND INFINITY
|سنة= 2010
|arxiv= 0912.3844
|class=math.CA}}</ref>{{,}}<ref>{{استشهاد بكتاب
|مؤلف= Marvin Ray Burns
|عنوان= RECORD CALCULATIONS OF THE MKB CONSTANT
|مسار= http://marvinrayburns.com/latest.html
| مسار أرشيف = https://web.archive.org/web/20190824210838/http://marvinrayburns.com/latest.html | تاريخ أرشيف = 24 أغسطس 2019 }}</ref>{{,}}<ref>{{استشهاد بكتاب
|مؤلف= Steven Finch
|عنوان= Errata and Addenda to Mathematical Constants
|صفحة= 63
|سنة= 2014
|ناشر= Harvard.edu
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf
| مسار أرشيف = https://web.archive.org/web/20160316175639/http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf | تاريخ أرشيف = 16 مارس 2016 }}</ref>
||
| bgcolor=#e0f0f0 align=center|<math> M_I </math>
||<math>\lim_{n\rightarrow \infty} \int_{1}^{2n} (-1)^x ~ \sqrt[x]{x} ~ dx = \int_{1}^{2n} e^{i \pi x} ~ x^{1/x} ~ dx </math>
||<syntaxhighlight lang="mathematica">lim_(2n->∞) int[1 to 2n] 
 {exp(i*Pi*x)*x^(1/x) dx}</syntaxhighlight>
|'''[[عدد مركب|خ]]'''
||{{OEIS2C|A255727}} <br /> {{OEIS2C|A255728}}
||[0;14,7,1,2,1,23,2,1,8,16,1,1,3,1,26,1,6,1,1, ...] <br /> - [0;1,2,6,13,41,112,1,25,1,1,1,1,3,13,2,1, ...] i
||2009
||<small> 0.07077603931152880353952802183028200 <br /> -0.68400038943793212918274445999266 '''''i''''' </small> 
|-

<!------------------------------------------v---------------------------------------->
|1.259921049894873164767 
||[[جذر تكعيبي|الجذر التكعيبي]] للرقم 2
||[[ملف:Riemann surface cube root.jpg|100px]]
| bgcolor=#e0f0f0 align=center|<math>\sqrt[3]{2}</math>
|| <math>\sqrt[3]{2}</math>
||<syntaxhighlight lang="mathematica">2^(1/3)</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A002580}}
||[1;3,1,5,1,1,4,1,1,8,1,14,1,10,2,1,4,12,2,3,...]
||
||<small> 1.25992104989487316476721060727822835 </small>
|-

<!------------------------------------------v----------------------------------------->
|1.09317045919549089396
||ثابت سمراندش 1ª <ref>{{استشهاد بكتاب
|مؤلف= Marius Coman
|سنة= 2013
|عنوان= The Math Encyclopedia of Smarandache type Notions: Vol. I. Number Theory
|مسار= http://archive.lib.msu.edu/crcmath/math/math/l/l146.htm
| مسار أرشيف = https://web.archive.org/web/20130621061642/http://archive.lib.msu.edu/crcmath/math/math/l/l146.htm | تاريخ أرشيف = 21 يونيو 2013 }}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{S_1}</math>
||<math>\sum_{n=2}^\infty \frac1{\mu(n)!} {\color{white}....\color{black}} </math> حيث ''μ''(''n'') هو دالة كيمبنر 
||
||
||{{OEIS2C|A048799}}
||[1;10,1,2,1,2,1,13,3,1,6,1,2,11,4,6,2,15,1,1,...]
||
||<small> 1.09317045919549089396820137014520832 </small>
|-

<!--------------------------------------------v---------------------------------------->
| 0.62481053384382658687 <br /> + 1.30024 25902 20120 419 ''i''
||[[كسر مستمر معمم|الكسر المستمر المعمم]] <br /> [[وحدة تخيلية|للوحدة التخليلية]] ''i'' 
||
| bgcolor=#e0f0f0 align=center|<math> {{F}_{CG}}_{(i)} </math>
|| <math> \textstyle i{+}\frac i{i+\frac i{i+\frac i{i+\frac i{i+\frac i{i+\frac i{i+i{/...}}}}}}} =
 \sqrt{\frac{\sqrt{17}-1}{8}} + i \left(\tfrac12 {+} \sqrt{\frac{2}{\sqrt{17}-1}}\right)</math>
||<syntaxhighlight lang="mathematica" >i+i/(i+i/(i+i/(i+i/(i+i/(
i+i/(i+i/(i+i/(i+i/(i+i/(
i+i/(i+i/(i+i/(i+i/(i+i/(
i+i/(i+i/(i+i/(i+i/(i+i/(
...)))))))))))))))))))))</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A156590}}<br /><br />{{OEIS2C|A156548}}
||[i;1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,i,1,..] <br />= [0;{{سطر فوقي|1,i}}] 
||
||<small> 0.62481053384382658687960444744285144 <br /> + 1.30024259022012041915890982074952 ''i'' </small>
|-

<!---------------------------------------v--------------------------------------------->
| 3.05940740534257614453
||ثابت المضروب <br /> المزدوج
||[[ملف:Double factorial.PNG|100px]]
| bgcolor=#e0f0f0 align=center|<math>{C_{_{n!!}}}</math>
||<math> \sum_{n=0}^{\infty} \frac{1}{n!!} = \sqrt{e} \left[\frac {1}{\sqrt{2}}+\gamma(\tfrac12 ,\tfrac12)\right]</math>
||<syntaxhighlight lang="mathematica">Sum[n=0 to ∞]{1/n!!}</syntaxhighlight>
||
||{{OEIS2C|A143280}}
||[3;16,1,4,1,66,10,1,1,1,1,2,5,1,2,1,1,1,1,1,2,...]
||
||<small> 3.05940740534257614453947549923327861 </small>
|-

<!-------------------------------------------v------------------------------------------>
|5.97798681217834912266 
||ثابت ماديلونغ <ref>{{استشهاد بكتاب 
|مؤلف1=David Borwein |مؤلف2=Jonathan M. Borwein |مؤلف3=Christopher Pinner  |last-author-amp=yes |عنوان= Convergence of Madelung-Like Lattice sums
|مسار= http://www.ams.org/journals/tran/1998-350-08/S0002-9947-98-01983-7/S0002-9947-98-01983-7.pdf
|سنة= 1998 
|ناشر= AMS
|isbn= 
|صفحة= Volume 350, Number 8, Pages 3131–3167
| مسار أرشيف = https://web.archive.org/web/20190504030929/https://www.ams.org/journals/tran/1998-350-08/S0002-9947-98-01983-7/S0002-9947-98-01983-7.pdf | تاريخ أرشيف = 4 مايو 2019 }}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{H}_{2}(2)</math>
||<math> \pi \ln(3) \sqrt 3 </math>
||<syntaxhighlight lang="mathematica">Pi Log[3]Sqrt[3]</syntaxhighlight>
||
||{{OEIS2C|A086055}}
||[5;1,44,2,2,1,15,1,1,12,1,65,11,1,3,1,1,...]
||
||<small> 5.97798681217834912266905331933922774 </small>
|-

<!------------------------------------------v----------------------------------------->
|0.91893853320467274178
||[[دالة غاما|صيغة راب]] <ref>{{استشهاد بأرخايف
|author= István Mezö
|year= 2011
|title= On the integral of the fourth Jacobi theta function
|arxiv= 1106.1042
|class=math.NT}}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{\zeta'(0)}</math>
||<math>\int\limits_a^{a+1}\log\Gamma(t)\,\mathrm dt = \tfrac12\log2\pi + a\log a - a,\quad a \ge 0</math>
||<syntaxhighlight lang="mathematica">integral_a^(a+1)
{log(Gamma(x))+a-a log(a)} dx</syntaxhighlight>
||
||{{OEIS2C|A075700}}
||[0;1,11,2,1,36,1,1,3,3,5,3,1,18,2,1,1,2,2,1,1,...]
||
||<small> 0.91893853320467274178032973640561763 </small>
|-

<!-------------------------------------v--------------------------------------------->
|2.20741609916247796230
||[[مسألة الأريكة المتحركة]] <ref>{{استشهاد بكتاب
|مؤلف= Steven Finch
|عنوان= Moving Sofa Constant
|مسار= http://mathcad.com/library/constants/sofa.htm
|سنة= 2007
|ناشر= Mathsoft
|مسار أرشيف= https://web.archive.org/web/20170804124839/https://web.archive.org/web/20080107101427/http://mathcad.com/library/constants/sofa.htm
|تاريخ أرشيف= 4 أغسطس 2017
|تاريخ الوصول= 5 سبتمبر 2019
|حالة المسار= dead
}}</ref>
||[[ملف:Hammersley sofa animated.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math>{S_{_{H}}}</math>
||<math> \frac {\pi}{2} +\frac {2}{\pi} \, </math> 
||<syntaxhighlight lang="mathematica">pi/2 + 2/pi</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A086118}}
||[2;4,1,4,1,1,2,5,1,11,1,1,5,1,6,1,3,1,1,1,1,7,...]
||1967
||<small> 2.20741609916247796230685674512980889 </small>
|-

<!------------------------------------------v----------------------------------------->
|1.17628081825991750654 
||عدد سالم،<ref>{{استشهاد بكتاب
|مؤلف= Pei-Chu Hu,Chung-Chun 
|سنة= 2008
|عنوان= Distribution Theory of Algebraic Numbers
|ناشر= Hong Kong University
|مسار= https://books.google.com/?id=LYT5sBm_Ie0C&lpg=PA247&dq=1.1762808&pg=PA246#v=onepage&q=1.1762808&f=false
|صفحة= 246
|isbn= 978-3-11-020536-7
|مسار أرشيف= https://web.archive.org/web/20200304172855/https://books.google.com/?id=LYT5sBm_Ie0C&lpg=PA247&dq=1.1762808&pg=PA246#v=onepage&q=1.1762808&f=false|تاريخ أرشيف=2020-03-04}}</ref>
تخيل ليمير
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{\sigma_{_{10}}}</math>
||<math>x^{10}+x^9-x^7-x^6-x^5-x^4-x^3+x+1 </math>
||<syntaxhighlight lang="mathematica">x^10+x^9-x^7-x^6 
 -x^5-x^4-x^3+x+1</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A073011}}
||[1;5,1,2,17,1,7,2,1,1,2,4,7,2,2,1,1,15,1,1, ...
||1983?
||<small> 1.17628081825991750654407033847403505 </small>
|-

<!--------------------------------------------v---------------------------------------->
| 0.37395581361920228805
||ثابت [[إميل أرتين]] <ref>{{استشهاد بكتاب
|مؤلف= Paulo Ribenboim
|عنوان= My Numbers, My Friends: Popular Lectures on Number Theory
|صفحة= 66
|سنة= 2000
|ناشر= Springer
|isbn= 0-387-98911-0
|مسار= https://books.google.com/?id=EiYvlcimEi4C&pg=PA66&dq=1.9287800#v=onepage&q=1.9287800&f=false
|مسار أرشيف= https://web.archive.org/web/20200304172858/https://books.google.com/?id=EiYvlcimEi4C&pg=PA66&dq=1.9287800#v=onepage&q=1.9287800&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{C}_{Artin}</math>
||<math>\prod_{n=1}^{\infty} \left(1-\frac{1}{p_n(p_n-1)}\right)\quad p_n \scriptstyle \text{ = prime} </math>
||<syntaxhighlight lang="mathematica">Prod[n=1 to ∞] 
 {1-1/(prime(n) 
 (prime(n)-1))}</syntaxhighlight>
||
||{{OEIS2C|A005596}}
||[0;2,1,2,14,1,1,2,3,5,1,3,1,5,1,1,2,3,5,46,...]
||1999
||<small> 0.37395581361920228805472805434641641 </small>
|-

<!---------------------------------------v--------------------------------------------->
|0.42215773311582662702 
||حجم رباعي الأسطح <ref>{{استشهاد بكتاب 
|عنوان= Volume and Surface area of the Spherical Tetrahedron (AKA Reuleaux tetrahedron) by geometrical methods
|مسار= http://www.math.unl.edu/~bharbourne1/ST/sphericaltetrahedron.html
|سنة= 2010
|ناشر= University of Nebraska–Lincoln
| مسار أرشيف = https://web.archive.org/web/20190816203834/http://www.math.unl.edu/~bharbourne1/ST/sphericaltetrahedron.html | تاريخ أرشيف = 16 أغسطس 2019 }}</ref>
||[[ملف:ReuleauxTetrahedron Animation.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math>{V_{_{R}}}</math>
||<math> \frac{s^3}{12}(3\sqrt2 - 49 \, \pi + 162 \, \arctan\sqrt2) </math>
||<syntaxhighlight lang="mathematica">(3*Sqrt[2] - 49*Pi + 162*ArcTan[Sqrt[2]])/12</syntaxhighlight>
||
||{{OEIS2C|A102888}}
||[0;2,2,1,2,2,7,4,4,287,1,6,1,2,1,8,5,1,1,1,1, ...]
||
||<small> 0.42215773311582662702336591662385075 </small>
|-

<!------------------------------------------v---------------------------------------->
|2.82641999706759157554
||ثابت موراتا <ref>{{استشهاد بكتاب 
|مؤلف= Leo Murata
|عنوان= On the Average of the Least Primitive Root Modulo p
|مسار= http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/0958-2.pdf
|سنة= 1996 
|ناشر= Meijigakuin University
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20160303190643/http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/0958-2.pdf | تاريخ أرشيف = 3 مارس 2016 }}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{C_m}</math>
||<math> \prod_{n = 1}^\infty \underset{p_{n}: \, {prime}}{ \Big(1 + \frac{1}{(p_n-1)^2}\Big)}</math>
||<syntaxhighlight lang="mathematica">Prod[n=1 to ∞]
{1+1/(prime(n)
-1)^2}</syntaxhighlight>
||
||{{OEIS2C|A065485}}
||[2;1,4,1,3,5,2,2,2,4,3,2,1,3,2,1,1,1,8,2,2,28,...]
||
||<small> 2.82641999706759157554639174723695374 </small>
|-

<!-----------------------------------------v------------------------------------------->
|1.09864196439415648573 
||ثابت باريس
||
| bgcolor=#e0f0f0 align=center|<math> C_{Pa} </math>
|| <math> \prod_{n=2}^\infty \frac{2 \varphi}{\varphi+ \varphi_n}  \; ,\; \varphi {=} {Fi}</math> &nbsp;con&nbsp; <math>\varphi_n {=} \sqrt{1 {+} \varphi_{n {-} 1}}</math> &nbsp; y &nbsp; <math>\varphi_1 {=} 1 </math>
||
||
||{{OEIS2C|A105415}}
||[1;10,7,3,1,3,1,5,1,4,2,7,1,2,3,22,1,2,5,2,1,...]
||
||<small> 1.09864196439415648573466891734359621 </small>
|-

<!----------------------------------------v----------------------------------------->
|2.39996322972865332223 <br /> [[راديان|بالراديان]]
||[[زاوية ذهبية|الزاوية الذهبية]] <ref>{{استشهاد بكتاب
|عنوان= Ángulo áureo  
|مسار= https://fibonacci.ucoz.com/index/ang/0-9
| مسار أرشيف = https://web.archive.org/web/20190403185232/http://fibonacci.ucoz.com/index/ang/0-9 | تاريخ أرشيف = 3 أبريل 2019 }}</ref>
|bgcolor=#ffffff align=center|[[ملف:Golden Angle.svg|50px]][[ملف:Sunflower.svg|50px]]
| bgcolor=#e0f0f0 align=center|<math>{b}</math>
||<math>(4-2\,\Phi)\,\pi = (3-\sqrt{5})\,\pi</math> = 137.5077640500378546 ...°
||<syntaxhighlight lang="mathematica">(4-2*Phi)*Pi</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A131988}}
||[2;2,1,1,1087,4,4,120,2,1,1,2,1,1,7,7,2,11,...]
||1907
||<small> 2.39996322972865332223155550663361385 </small>
|-

<!-----------------------------------------v----------------------------------------->
| 1.64218843522212113687 
||ثابت ليبيسج <ref>{{استشهاد بكتاب
|مؤلف= Eric W. Weisstein 
|سنة= 1999
|عنوان= Lebesgue Constants (Fourier Series)
|ناشر= Michigan State University Libraries
|مسار= http://archive.lib.msu.edu/crcmath/math/math/l/l146.htm
| مسار أرشيف = https://web.archive.org/web/20130621061642/http://archive.lib.msu.edu/crcmath/math/math/l/l146.htm | تاريخ أرشيف = 21 يونيو 2013 }}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{L2}</math>
||<math>\frac{1}{5} + \frac{\sqrt{25-2\sqrt{5}}}{\pi} = \frac{1}{\pi} \int_0^\pi \frac {\left|\sin(\frac{5t}{2})\right|} {\sin(\frac{t}{2})} \,d t </math>
||<syntaxhighlight lang="mathematica">1/5 + sqrt(25 - 
 2*sqrt(5))/Pi</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A226655}}
||[1;1,1,1,3,1,6,1,5,2,2,3,1,2,7,1,3,5,2,2,1,1,...]
||1910
||<small> 1.64218843522212113687362798892294034 </small>
|-

<!-----------------------------------------v----------------------------------------->
|1.26408473530530111307 
||ثابت فارديt<ref>{{استشهاد بكتاب
|مؤلف= saildart
|عنوان= Vardi
|مسار= http://www.saildart.org/CHAP4.ANS[GKP,DEK]1
| مسار أرشيف = https://web.archive.org/web/20160911201939/http://saildart.org/CHAP4.ANS[GKP,DEK]1 | تاريخ أرشيف = 11 سبتمبر 2016 }}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{V_c}</math>
||<math>\frac{\sqrt{3}}{\sqrt{2}}\prod_{n\ge1}\left(1+{1\over(2e_n-1)^2}\right)^{\!1/2^{n+1}} </math>
||
||
||{{OEIS2C|A076393}}
||[1;3,1,3,1,2,5,54,7,1,2,1,2,3,15,1,2,1,1,2,1,...]
||1991
||<small> 1.26408473530530111307959958416466949 </small>
|-

<!-----------------------------------------v----------------------------------------->
|{{فجوات|1.50659|18849}} ± {{فجوات|0.00000|00028}}
||مساحة [[مجموعة ماندلبرو]] <ref>{{استشهاد بكتاب
|مؤلف= Robert P. Munafo
|عنوان= Pixel Counting  
|سنة= 2012
|مسار= http://www.mrob.com/pub/muency/pixelcounting.html
| مسار أرشيف = https://web.archive.org/web/20190810111304/http://www.mrob.com/pub/muency/pixelcounting.html | تاريخ أرشيف = 10 أغسطس 2019 }}</ref>
|bgcolor=#ffffff align=center|[[ملف:Mandelbrot sequence new.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math>\gamma </math>
|| <math>\sqrt{6\pi -1} - e = 1.506591651\cdots </math> 
||
||
||{{OEIS2C|A098403}}
||[1;1,1,37,2,2,1,10,1,1,2,2,4,1,1,1,1,5,4,...]
||1912
||<small> 1.50659177 +/- 0.00000008 </small>
|-

<!------------------------------------------v----------------------------------------->
|1.6111149258083
|| ثابت المضروب الأسي 
||
| bgcolor=#e0f0f0 align=center|<math>{S_{Ef}}</math>
||<math>\sum_{n=1}^{\infty} \frac{1}{n^{(n{-}1)^{\cdot^{\cdot^{\cdot^{2^1}}}}}} = 1 {+} \frac{1}{2^{1}} {+} \frac{1}{3^{2^{1}}} + \frac{1}{4^{3^{2^{1}}}} + \frac{1}{5^{4^{3^{2^{1}}}}} {+} \cdots</math>
||
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A080219}}
||[1; 1, 1, 1, 1, 2, 1, 808, 2, 1, 2, 1, 14,...]
||
||<small> 1.61111492580837673611111111111111111 </small>
|-

<!--------------------------------------------v----------------------------------------->
|1.11786415118994497314 
||ثابت جوه شموتز <ref>{{استشهاد بكتاب
|مؤلف= Steven R. Finch
|عنوان= Mathematical Constants
|صفحة= 287
|سنة= 2003
|ناشر= Cambridge University Press
|isbn= 3-540-67695-3
|مسار= https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA556&dq=Goh-Schmutz#v=onepage&q=Schmutz&f=false
|مسار أرشيف= https://web.archive.org/web/20200304172820/https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA556&dq=Goh-Schmutz#v=onepage&q=Schmutz&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math> C_{GS} </math>
||<math> \int^\infty_0\frac{\log(s+1)}{e^s-1} \ ds =
\! - \! \sum_{n=1}^\infty \frac {e^n}{n} Ei(-n)
</math>

||<syntaxhighlight lang="mathematica">Integrate{
log(s+1)
/(E^s-1)}</syntaxhighlight> 
||
||{{OEIS2C|A143300}}
||[1;8,2,15,2,7,2,1,1,1,1,2,3,5,3,5,1,1,4,13,1,...]
||
||<small> 1.11786415118994497314040996202656544 </small>
|-

<!------------------------------------------------v---------------------------------------->
|0.3181315052047641 <br />
±1.337235701430689 
||النقط الثابتة على<br />[[لوغاريتم|اللوغاريتم]] الأكبر<ref>{{استشهاد بكتاب
|مؤلف= Dmitrii Kouznetsov
|عنوان= SOLUTION OF F(z + 1) = exp F(z) IN COMPLEX z-PLANE
|سنة= 2009
|ناشر= Institute for Laser Science (ILS), (UEC). Japan
|مسار= http://www.ils.uec.ac.jp/~dima/PAPERS/2009analuxpRepri.pdf
| مسار أرشيف = https://web.archive.org/web/20160304031238/http://www.ils.uec.ac.jp/~dima/PAPERS/2009analuxpRepri.pdf | تاريخ أرشيف = 4 مارس 2016 }}</ref>{{,}}
||[[ملف:Slogez01.jpg|100px]]
| bgcolor=#e0f0f0 align=center|<math> {-W(-1)} </math>
||<math>\lim_{n\rightarrow \infty}</math><math> f(x) = \underbrace{\log(\log(\log(\log(\cdots\log(\log(x)))))) \,\! }\atop {\log_s \text{ n times}} </math>
تختلف القيمة الابتدائية ل{{Mvar|x}} لتصبح <math display="inline"> 0, 1, e, e^e, e^{e^e}
</math>, etc.
||<code>-W(-1)</code><br/>
|'''[[عدد مركب|خ]]'''
||{{OEIS2C|A059526}} <br /> {{OEIS2C|A059527}}
||[-i;1 +2i,1+i,6-i,1+2i,-7+3i,2i,2,1-2i,-1+i,-, ...]
||
||<small> 0.31813150520476413531265425158766451 <br /> -1.33723570143068940890116214319371 '''''i''''' </small> 
|-

<!------------------------------------------v------------------------------------------>
|0.28016949902386913303
||ثابت [[سيرغي ناتانوفيتش بيرنشتين|بيرنشتين]] <ref>{{استشهاد بكتاب
|مؤلف= Lloyd N. Trefethen
|عنوان= Approximation Theory and Approximation Practice
|صفحة= 211
|سنة= 2013
|ناشر= SIAM
|isbn= 978-1-611972-39-9
|مسار= https://books.google.com/?id=En41UGQ6YXsC&lpg=PA210&dq=0.28016949902386913303643649&pg=PA211#v=onepage&q=0.28016949902386913303643649&f=false
|مسار أرشيف= https://web.archive.org/web/20200304172900/https://books.google.com/?id=En41UGQ6YXsC&lpg=PA210&dq=0.28016949902386913303643649&pg=PA211#v=onepage&q=0.28016949902386913303643649&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{\beta}</math>
||<math> \approx \frac {1}{2\sqrt {\pi}}</math>
||<syntaxhighlight lang="mathematica">1/(2 sqrt(pi))</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A073001}}
||[0;3,1,1,3,9,6,3,1,3,14,34,2,1,1,60,2,2,1,1,...]
||1913
||<small> 0.28016949902386913303643649123067200 </small>
|-

<!------------------------------------------v------------------------------------------>
| 0.66016181584686957392
||ثابت [[عددان أوليان توأم|العددان الأوليان التوأمان]] <ref>{{استشهاد بأرخايف
|مؤلف= R. M. ABRAROV AND S. M. ABRAROV
|عنوان= PROPERTIES AND APPLICATIONS OF THE PRIME DETECTING FUNCTION
|arxiv= 1109.6557
|class= math.GM
}}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{C}_{2}</math>
||<math>\prod_{p=3}^\infty \frac{p(p-2)}{(p-1)^2} </math>
||<syntaxhighlight lang="mathematica">prod[p=3 to ∞]
{p(p-2)/(p-1)^2</syntaxhighlight>
||
||{{OEIS2C|A005597}}
||[0;1,1,1,16,2,2,2,2,1,18,2,2,11,1,1,2,4,1,...]
||1922
||<small> 0.66016181584686957392781211001455577 </small>
|-

<!-------------------------------------------v----------------------------------------->
|1.22674201072035324441
||ثابت معامل فيبوناتشي <ref>{{استشهاد بكتاب 
|مؤلف1=Sergey Kitaev  |مؤلف2=Touﬁk Mansour
 |lastauthoramp=yes |عنوان= The problem of the pawns
|مسار= http://drakkar.math.uqam.ca/~plouffe/references/0305253.pdf
|سنة= 2007
| مسار أرشيف = https://web.archive.org/web/20150413153440/http://drakkar.math.uqam.ca/~plouffe/references/0305253.pdf | تاريخ أرشيف = 13 أبريل 2015 }}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>F </math>
|| <math> \prod_{n = 1}^\infty \left(1 - \left( -\frac{1}{{\varphi}^2}\right)^n \right)=
\prod_{n = 1}^\infty \left(1 - \left( \frac{\sqrt{5}-3}{2}\right)^n \right)</math>
||<syntaxhighlight lang="mathematica">prod[n=1 to ∞] 
 {1-((sqrt(5) -3)/2)^n}</syntaxhighlight>
||
||{{OEIS2C|A062073}}
||[1;4,2,2,3,2,15,9,1,2,1,2,15,7,6,21,3,5,1,23,...]
||
||<small> 1.22674201072035324441763023045536165 </small>
|-

<!-------------------------------------------v---------------------------------------->
|0.11494204485329620070 
||ثابت [[يوهانس كيبلر|كيبلر]]-بووكمب <ref>{{استشهاد بأرخايف 
|author= Richard J. Mathar
|title= Circumscribed Regular Polygons
|arxiv=1301.6293
|year= 2013
|class= math.MG
}}</ref>
|bgcolor=#ffffff align=center|[[ملف:Regular polygons qtl4.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\rho}</math>
||<math> \prod_{n=3}^\infty \cos\left(\frac{\pi}{n} \right) = \cos\left(\frac{\pi}{3} \right) \cos\left(\frac{\pi}{4} \right) \cos\left(\frac{\pi}{5}\right) ...</math>
||<syntaxhighlight lang="mathematica">prod[n=3 to ∞]
{cos(pi/n)}</syntaxhighlight>
||<br /><br /><br />
||{{OEIS2C|A085365}}
||[0;8,1,2,2,1,272,2,1,41,6,1,3,1,1,26,4,1,1,...]
||
||<small> 0.11494204485329620070104015746959874 </small>
|-

<!------------------------------------------v----------------------------------------->
|1.78723165018296593301 
||ثابت كومورنيك-لوريتي <ref>{{استشهاد بكتاب
|مؤلف= Christoph Lanz
|عنوان= k-Automatic Reals
|ناشر= Technischen Universität Wien
|مسار= http://dmg.tuwien.ac.at/drmota/DiplomarbeitLanz.pdf
| مسار أرشيف = https://web.archive.org/web/20160304085934/http://dmg.tuwien.ac.at/drmota/DiplomarbeitLanz.pdf | تاريخ أرشيف = 4 مارس 2016 }}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{q}</math>
||<math>1 = \!\sum_{n=1}^\infty \frac{t_k}{q^k} \qquad \scriptstyle \text{Raiz real de} \displaystyle\prod_{n=0}^\infty \!\left (\! 1 {-} \frac{1}{q^{2^n}} \!\right) \! {+} \frac{q{-}2}{q{-}1}=0</math>
||<syntaxhighlight lang="mathematica">FindRoot[(prod[n=0 to ∞] 
{1-1/(x^2^n)}+(x-2)
/(x-1))= 0, {x, 1.7}, 
WorkingPrecision->30]</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A055060}}
||[1;1,3,1,2,3,188,1,12,1,1,22,33,1,10,1,1,7,...]
||1998
||<small> 1.78723165018296593301327489033700839 </small>
|-

<!------------------------------------------v------------------------------------------>
|3.30277563773199464655
||القيمة البرونزية <ref>{{استشهاد بكتاب 
|عنوان= NÚMERO DE BRONCE. PROPORCIÓN DE BRONCE
|مسار= http://www.grupoalquerque.es/ferias/2013/archivos/metalicos/material/Numeros_metalicos_bronce.pdf
|سنة=  
|ناشر= 
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20160606223515/http://www.grupoalquerque.es/ferias/2013/archivos/metalicos/material/Numeros_metalicos_bronce.pdf | تاريخ أرشيف = 6 يونيو 2016 }}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{\sigma}_{\,Rr} </math>
||<math>\frac {3+\sqrt{13}}{2} = 1+\sqrt{3+\sqrt{3+\sqrt{3+\sqrt{3+\cdots}}}} </math>
||<syntaxhighlight lang="mathematica">(3+sqrt 13)/2</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A098316}}
||[3;3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,...] <br /> = [3;{{سطر فوقي|3}},...]
||
||<small> 3.30277563773199464655961063373524797 </small>
|-

<!------------------------------------------v---------------------------------------->
|0.82699334313268807426 
||تغطية القرص <ref>{{استشهاد بأرخايف
|مؤلف= SERGI ELIZALDE
|عنوان= ASYMPTOTIC ENUMERATION OF PERMUTATIONS AVOIDING GENERALIZED PATTERNS
|arxiv=math/0505254
|سنة=2005
}}</ref>
|bgcolor=#ffffff align=center|[[ملف:COVER5.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math>{C_5}</math>
||<math>{\frac{1}{{\sum\limits_{n=0}^\infty \frac{1}{\binom{3n+2}{2}}}}}=\frac{3\sqrt3}{2\pi}</math>
||<syntaxhighlight lang="mathematica">3 Sqrt[3]/(2 Pi)</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A086089}}
||[0;1,4,1,3,1,1,4,1,2,2,1,1,7,1,4,4,2,1,1,1,1,...]
||1939 <br /> 1949
||<small> 0.82699334313268807426698974746945416 </small>
|-

<!------------------------------------------v------------------------------------------>
|2.66514414269022518865 
||[[ثابتة غيلفوند–شنايدر]] <ref>{{استشهاد بكتاب 
|مؤلف= David Cohen
|عنوان= Precalculus: With Unit Circle Trigonometry
|مسار= https://books.google.com/?id=RSU8AAAAQBAJ&lpg=PA328&dq=2.6651&pg=PA328#v=onepage&q=2.6651&f=false
|سنة= 2006
|isbn= 0-534-40230-5
|ناشر= Thomson Learning Inc.
|صفحة= 328
|مسار أرشيف= https://web.archive.org/web/20200304172902/https://books.google.com/?id=RSU8AAAAQBAJ&lpg=PA328&dq=2.6651&pg=PA328#v=onepage&q=2.6651&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math> G_{\,GS} </math>
||<math>2^{\sqrt{2}}</math>
||<syntaxhighlight lang="mathematica">2^sqrt{2}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A007507}}
||[2;1,1,1,72,3,4,1,3,2,1,1,1,14,1,2,1,1,3,1,...]
||1934
||<small> 2.66514414269022518865029724987313985 </small>
|-

<!----------------------------------------v-------------------------------------------->
|3.27582291872181115978 
||ثابت ليفي <ref>{{استشهاد بأرخايف
|author= Marek Wolf
|title= Two arguments that the nontrivial zeros of the Riemann zeta function are irrational
|arxiv=1002.4171
|year= 2010
|class=math.NT
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>\gamma </math>
|| <math> e^{\pi^2/(12\ln2)}</math>
||<syntaxhighlight lang="mathematica">e^(\pi^2/(12 ln(2))</syntaxhighlight>
||
||{{OEIS2C|A086702}}
||[3;3,1,1,1,2,29,1,130,1,12,3,8,2,4,1,3,55,...]
||1936
||<small> 3.27582291872181115978768188245384386 </small>
|-

<!------------------------------------------v----------------------------------------->
|0.52382257138986440645
||دالة تشي
|bgcolor=#ffffff align=center|[[ملف:Chi function.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\operatorname{Chi()}}</math>
||<br /><math>\gamma + \int_0^x\frac{\cosh t-1}{t}\,dt </math>
<math> \scriptstyle \gamma \, \text{= 0.5772156649...}</math>
||<syntaxhighlight lang="mathematica">Chi(x)</syntaxhighlight>
||
||{{OEIS2C|A133746}}
||[0;1,1,9,1,172,1,7,1,11,1,1,2,1,8,1,1,1,1,1,...]
||
||<small> 0.52382257138986440645095829438325566 </small>
|-

<!-------------------------------------------v----------------------------------------->
|1.1319882487943 
||ثابت فيسونث<ref>{{استشهاد بكتاب 
|مؤلف= DIVAKAR VISWANATH
|عنوان= RANDOM FIBONACCI SEQUENCES AND THE NUMBER 1.13198824...
|مسار= http://www.ams.org/journals/mcom/2000-69-231/S0025-5718-99-01145-X/S0025-5718-99-01145-X.pdf
|سنة= 1999 
|ناشر= MATHEMATICS OF COMPUTATION 
| مسار أرشيف = https://web.archive.org/web/20190502183717/https://www.ams.org/journals/mcom/2000-69-231/S0025-5718-99-01145-X/S0025-5718-99-01145-X.pdf | تاريخ أرشيف = 2 مايو 2019 }}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{C}_{Vi}</math>
||<math>\lim_{n \to \infty}|a_n|^\frac{1}{n}</math> &nbsp;&nbsp;&nbsp;&nbsp; <br />
حيث''a<sub>n</sub>'' = [[عدد فيبوناتشي]]
||<syntaxhighlight lang="mathematica">lim_(n->∞) 
|a_n|^(1/n)</syntaxhighlight> 
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A078416}} 
||[1;7,1,1,2,1,3,2,1,2,1,8,1,5,1,1,1,9,1,...]
||1997
|| 1.1319882487943 
|-

<!-------------------------------------------v----------------------------------------->
|1.23370055013616982735
||ثابت فاراد <ref>{{استشهاد بكتاب 
|مؤلف1=Helmut Brass |مؤلف2=Knut Petras |عنوان= Quadrature Theory: The Theory of Numerical Integration on a Compact Interval
|مسار= https://books.google.com/?id=nbjOnJlJfFYC&pg=PA274&dq=Favard+Constant#v=onepage&q=Favard%20Constant&f=false
|سنة= 2010  
|ناشر= AMS
|isbn= 978-0-8218-5361-0
|صفحة= 274
|مسار أرشيف= https://web.archive.org/web/20200304172905/https://books.google.com/?id=nbjOnJlJfFYC&pg=PA274&dq=Favard+Constant#v=onepage&q=Favard%20Constant&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>\tfrac34\zeta(2)</math>
||<math> \frac{\pi^2}{8} = \sum_{n = 0}^\infty \frac{1}{(2n-1)^2} = \frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+\cdots </math>
||<syntaxhighlight lang="mathematica">sum[n=1 to ∞]
{1/((2n-1)^2)}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A111003}}
||[1;4,3,1,1,2,2,5,1,1,1,1,2,1,2,1,10,4,3,1,1,...]
||1902 <br /> a <br /> 1965
||<small> 1.23370055013616982735431137498451889 </small>
|-

<!---------------------------------------v-------------------------------------------->
|2.50662827463100050241
||[[جذر تربيعي|الجذر التربيعي]] ل 2 [[ط (رياضيات)|باي]]
||[[ملف:Stirling's Approximation Small.png|100px]] 
| bgcolor=#e0f0f0 align=center|<math>\sqrt{2 \pi} </math>
|| <math>\sqrt{2 \pi} = \lim_{n \to \infty} \frac {n! \; e^n}{n^n \sqrt{n}}{\color{white}....\color{black}}</math> <br />
''[[تقريب ستيرلينغ]]''
||<syntaxhighlight lang="mathematica">sqrt (2 pi)</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A019727}}
||[2;1,1,37,4,1,1,1,1,9,1,1,2,8,6,1,2,2,1,3,...]
||1692 <br /> a <br /> 1770
||<small> 2.50662827463100050241576528481104525 </small>
|-

<!------------------------------------------v----------------------------------------->
|4.13273135412249293846
||الجذر التربيعي ل[[تاو]]* [[دالة أسية|مشتقة الدالة الأسية للأساس e]]
||<br /><br />
| bgcolor=#e0f0f0 align=center|<math> \sqrt{\tau e}</math>
||<math> \sqrt{2 \pi e}</math>
||<syntaxhighlight lang="mathematica">sqrt(2 pi e)</syntaxhighlight>
||
||{{OEIS2C|A019633}}
||[4;7,1,1,6,1,5,1,1,1,8,3,1,2,2,15,2,1,1,2,4,...]
||
||<small> 4.13273135412249293846939188429985264 </small>
|-

<!--------------------------------------v---------------------------------------------->
|0.97027011439203392574 
||ثابت لوتش <ref>{{استشهاد بكتاب 
|مؤلف= Steven Finch
|عنوان= Continued Fraction Transformation
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/kz.pdf
|سنة= 2007
|ناشر= Harvard University
|صفحة= 7
| مسار أرشيف = https://web.archive.org/web/20160419114446/http://www.people.fas.harvard.edu/~sfinch/csolve/kz.pdf | تاريخ أرشيف = 19 أبريل 2016 }}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{\text{£}_{_{Lo}}}</math>
||<math> \frac {6 \ln 2 \ln 10}{ \pi^2} </math>
||<syntaxhighlight lang="mathematica">6*ln(2)*ln(10)/Pi^2</syntaxhighlight>
||
||{{OEIS2C|A086819}}
||[0;1,32,1,1,1,2,1,46,7,2,7,10,8,1,71,1,37,1,1,...]
||1964
||<small> 0.97027011439203392574025601921001083 </small>
|-

<!--------------------------------------v--------------------------------------------->
| 0.98770039073605346013 
||المساحة المحيطة ل[[مثلث رولو]] <ref>{{استشهاد بكتاب 
|مؤلف= Clifford A. Pickover
|عنوان= The Math Book
|مسار= https://books.google.com/?id=JrslMKTgSZwC&lpg=PA266&dq=0.9877003907&pg=PA266#v=onepage&q=0.9877003907&f=false
|ناشر= Sterling Publishing
|isbn= 978-1-4027-5796-9
|صفحة= 266
|سنة= 2009
|مسار أرشيف= https://web.archive.org/web/20200615015843/https://books.google.com/books?id=JrslMKTgSZwC&lpg=PA266&dq=0.9877003907&pg=PA266&hl=en#v=onepage&q=0.9877003907&f=false|تاريخ أرشيف=2020-03-04}}</ref> 
|bgcolor=#ffffff align=center|[[ملف:Rotation of Reuleaux triangle.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math>\mathcal{T}_R</math>
||<math> a^2 \cdot \left( 2\sqrt{3} + {\frac{\pi}{6}} - 3 \right)</math> &nbsp;&nbsp; <br />
حيث ''a''= طول ضلع المربع
||<syntaxhighlight lang="mathematica">2 sqrt(3)+pi/6-3</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A066666}}
||[0;1,80,3,3,2,1,1,1,4,2,2,1,1,1,8,1,2,10,1,2,...]
||1914
||<small> 0.98770039073605346013199991355832854 </small>
|-

<!--------------------------------------v---------------------------------------------->
|0.70444220099916559273 
||ثابت الإهمال <sub>2</sub> <ref>{{استشهاد بكتاب 
|مؤلف= Steven Finch
|عنوان= Unitarism and Infinitarism
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/try.pdf
|سنة= 2004
|ناشر= Harvard.edu
|صفحة= 1
| مسار أرشيف = https://web.archive.org/web/20160304041318/http://www.people.fas.harvard.edu/~sfinch/csolve/try.pdf | تاريخ أرشيف = 4 مارس 2016 }}</ref>
|<br /><br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>\mathcal{C}_2</math>
||<math> \underset{ p_n: \, {prime}}{\prod_{n = 1}^\infty \left(1 - \frac{1}{p_n(p_n+1)}\right)} </math>
||<syntaxhighlight lang="mathematica">N[prod[n=1 to ∞] 
 {1 - 1/(prime(n)* 
 (prime(n)+1))}]</syntaxhighlight>
||
||{{OEIS2C|A065463}}
||[0;1,2,2,1,1,1,1,4,2,1,1,3,703,2,1,1,1,3,5,1,...]
||
||<small> 0.70444220099916559273660335032663721 </small>
|-

<!--------------------------------------- v ------------------------------------------->
|1.84775906502257351225 
||معامل الربط <ref>{{استشهاد بكتاب 
|مؤلف= Mireille Bousquet-Mélou | مؤلف-وصلة = Mireille Bousquet-Mélou
|عنوان= Two-dimensional self-avoiding walks
|مسار= https://www.labri.fr/perso/bousquet/Exposes/fpsac-saw.pdf
|ناشر= CNRS, LaBRI, Bordeaux, France
| مسار أرشيف = https://web.archive.org/web/20180328164709/http://www.labri.fr/perso/bousquet/Exposes/fpsac-saw.pdf | تاريخ أرشيف = 28 مارس 2018 }}</ref><ref>{{استشهاد بكتاب 
|مؤلف1=Hugo Duminil-Copin  |مؤلف2=Stanislav Smirnov
 |lastauthoramp=yes |عنوان= The connective constant of the honeycomb lattice √ (2 + √ 2)
|مسار= http://www.unige.ch/~smirnov/slides/slides-saw.pdf
|سنة= 2011
|ناشر= Université de Geneve
| مسار أرشيف = https://web.archive.org/web/20150714034525/http://www.unige.ch/~smirnov/slides/slides-saw.pdf | تاريخ أرشيف = 14 يوليو 2015 }}</ref>
|bgcolor=#ffffff align=center|[[ملف:HEX-LATTICE-20.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\mu}</math>
||<math>\sqrt{2 + \sqrt{2}} \; = \lim_{n \rightarrow \infty} c_n^{1/n} </math>
دالة [[متعددة الحدود]]:<br />
<math> \; x ^ 4-4 x ^ 2 + 2=0</math>
||<syntaxhighlight lang="mathematica">sqrt(2+sqrt(2))</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A179260}}
||[1;1,5,1,1,3,6,1,3,3,10,10,1,1,1,5,2,3,1,1,3,...]
||
||<small> 1.84775906502257351225636637879357657 </small>
|-

<!------------------------------------------v------------------------------------------>
| 0.30366300289873265859 
||ثابت جاووس-كوزمين-يرسينغ <ref>{{استشهاد بكتاب
|مؤلف= W.A. Coppel
|عنوان= Number Theory: An Introduction to Mathematics
|صفحة= 480
|سنة= 2000
|ناشر= Springer
|isbn= 978-0-387-89485-0
|مسار= https://books.google.com/?id=We5FAAAAQBAJ&lpg=PA480&dq=0.303663&pg=PA480#v=onepage&q=0.303663&f=false
|مسار أرشيف= https://web.archive.org/web/20200304172909/https://books.google.com/books?id=We5FAAAAQBAJ&lpg=PA480&dq=0.303663&pg=PA480&hl=en#v=onepage&q=0.303663&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{\lambda}_{2}</math>
||<math>\lim_{n \to \infty}\frac{F_n(x) - \ln(1 - x)}{(-\lambda)^n} = \Psi(x),</math>
حيث <math>\Psi(x)</math> [[دالة تحليلية]] و<br />
<math>\Psi(0) \!=\! \Psi(1) \!=\! 0</math>.
||
||
||{{OEIS2C|A038517}}
||[0;3,3,2,2,3,13,1,174,1,1,1,2,2,2,1,1,1,2,2,1,...]
||1973
||<small> 0.30366300289873265859744812190155623 </small>
|-

<!------------------------------------------v----------------------------------------->
|1.57079632679489661923 
||ثابت فارد K1 <br /> [[جداء واليس]] <ref>{{استشهاد بكتاب 
|مؤلف= James Stuart Tanton
|عنوان= Encyclopedia of Mathematics
|مسار= https://books.google.com/?id=MfKKMSuthacC&pg=PA529&dq=wallis+product#v=onepage&q=wallis%20product&f=false
|سنة= 2005
|ناشر= 
|isbn=9781438110080
|صفحة= 529
|مسار أرشيف= https://web.archive.org/web/20200304172911/https://books.google.com/books?id=MfKKMSuthacC&pg=PA529&dq=wallis+product&hl=en#v=onepage&q=wallis%20product&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Wallis product-chart.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\frac{\pi}{2}}</math>
||<math> \prod_{n=1}^{\infty} \left(\frac{4n^2}{4n^2 - 1}\right) = \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \cdots </math>
||<syntaxhighlight lang="mathematica">Prod[n=1 to ∞] 
 {(4n^2)/(4n^2-1)}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A069196}}
||[1;1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,1,5,1...]
||1655
||<small> 1.57079632679489661923132169163975144 </small>
|-

<!------------------------------------------v----------------------------------------->
| 1.606695152415291763
||ثابت [[بول إيردوس|إيردوس]] بروين<ref>{{استشهاد بأرخايف 
|author= Robert Baillie
|title= Summing The Curious Series of Kempner and Irwin
|arxiv= 0806.4410
|class=math.CA
|year= 2013
}}</ref><ref>{{استشهاد بكتاب 
|مؤلف= Leonhard Euler
|عنوان= Consideratio quarumdam serierum, quae singularibus proprietatibus sunt praeditae
|مسار= http://eulerarchive.maa.org//pages/E190.html
|سنة= 1749
|صفحة= 108 
| مسار أرشيف = https://web.archive.org/web/20110623184135/http://www.math.dartmouth.edu/~euler/pages/E190.html | تاريخ أرشيف = 23 يونيو 2011 }}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{E}_{\,B}</math>
||<math>\sum_{m=1}^{\infty} \sum_{n=1}^{\infty}\frac{1}{2^{mn}} =\sum_{n=1}^{\infty}\frac{1}{2^n-1} = \frac{1}{1} \! + \! \frac{1}{3} \! + \! \frac{1}{7} \! + \! \frac{1}{15} \! + \! ...</math>
||<syntaxhighlight lang="mathematica">sum[n=1 to ∞]
{1/(2^n-1)}</syntaxhighlight>
|'''[[عدد غير كسري|غ.ك]]'''
||{{OEIS2C|A065442}}
||[1;1,1,1,1,5,2,1,2,29,4,1,2,2,2,2,6,1,7,1,...]
||1949 
||<small> 1.60669515241529176378330152319092458 </small>
|-

<!----------------------------------------------v------------------------------------------->
|1.61803398874989484820 
||[[في (حرف يوناني)|فاي]]، [[نسبة ذهبية|النسبة الذهبية]] <ref>{{استشهاد بكتاب 
|مؤلف1=Timothy Gowers |مؤلف2=June Barrow-Green |مؤلف3=Imre Leade |عنوان= The Princeton Companion to Mathematics
|مسار= https://books.google.com/?id=ZOfUsvemJDMC&lpg=PA316&dq=1.618033988749894848&pg=PA316#v=onepage&q=1.618033988749894848&f=false
|سنة= 2007
|ناشر= Princeton University Press
|isbn= 978-0-691-11880-2 
|صفحة= 316
|مسار أرشيف= https://web.archive.org/web/20200304172913/https://books.google.com/?id=ZOfUsvemJDMC&lpg=PA316&dq=1.618033988749894848&pg=PA316#v=onepage&q=1.618033988749894848&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Animation GoldenerSchnitt.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\varphi}</math>
|| <math>\frac{1 + \sqrt{5}}{2} = \sqrt{1 + \sqrt{1 + \sqrt{1 + \sqrt{1 + \cdots}}}} </math>
||<syntaxhighlight lang="mathematica">(1+5^(1/2))/2</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A001622}}
||[0;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,...]<br /> = [0;{{سطر فوقي|1}},...]
||-300 ~
||<small> 1.61803398874989484820458683436563811 </small>
|-

<!-----------------------------------------v---------------------------------------------->
|1.64493406684822643647 
||دالة ريمان زيتا (2)
||
| bgcolor=#e0f0f0 align=center|<math>{\zeta}(\,2)</math>
||<math> \frac{\pi^2}{6} = \sum_{n=1}^\infty\frac{1}{n^2} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots</math>
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞]
{1/n^2}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A013661}}
||[1;1,1,1,4,2,4,7,1,4,2,3,4,10 1,2,1,1,1,15,...]
||1826 <br /> to <br /> 1866
||<small> 1.64493406684822643647241516664602519 </small>
|-

<!----------------------------------------------v------------------------------------------->
| 1.73205080756887729352
||[[الجذر التربيعي ل 3]]<ref>{{استشهاد بكتاب 
|مؤلف= Vijaya AV
|عنوان= Figuring Out Mathematics
|مسار= https://books.google.com/?id=xAwukpHCqH0C&pg=PA15&dq=1.732050807#v=onepage&q=1.732050807&f=false
|سنة= 2007
|ناشر= Dorling Kindcrsley (India) Pvt. Lid.
|isbn= 978-81-317-0359-5 
|صفحة= 15
|مسار أرشيف= https://web.archive.org/web/20200304172915/https://books.google.com/?id=xAwukpHCqH0C&pg=PA15&dq=1.732050807#v=onepage&q=1.732050807&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Square root of 3 in cube.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>\sqrt{3} </math>
||<math> \sqrt[3]{3 \,\sqrt[3]{3 \, \sqrt[3]{3 \,\sqrt[3]{3 \,\sqrt[3]{3  \,\cdots}}}}} </math>
||<syntaxhighlight lang="mathematica">(3(3(3(3(3(3(3) 
 ^1/3)^1/3)^1/3) 
 ^1/3)^1/3)^1/3) 
 ^1/3 ...</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A002194}}
||[1;1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,...] <br /> = [1;{{سطر فوقي|1,2}},...]
||-465 <br /> to <br /> -398
||<small> 1.73205080756887729352744634150587237 </small>
|-

<!---------------------------------------------v---------------------------------------------->
|1.75793275661800453270
||عدد كاسنر
||
| bgcolor=#e0f0f0 align=center|<math>{R}</math>
||<math>\sqrt{1 + \sqrt{2 + \sqrt{3 + \sqrt{4 + \cdots}}}} </math>
|| <syntaxhighlight lang="mathematica">Fold[Sqrt[#1+#2]
 &,0,Reverse 
 [Range[20]]]</syntaxhighlight>
||
||{{OEIS2C|A072449}}
||[1;1,3,7,1,1,1,2,3,1,4,1,1,2,1,2,20,1,2,2,...]
||1878 <br /> a <br /> 1955
||<small> 1.75793275661800453270881963821813852 </small>
|-

<!--------------------------------------------v------------------------------------------>
|2.29558714939263807403
||ثابت القطع المكافئ العالمي <ref>{{استشهاد بكتاب
|مؤلف= Steven Finch
|عنوان= Errata and Addenda to Mathematical Constants
|صفحة= 59
|سنة= 2014
|ناشر= Harvard.edu
|isbn= 
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf
| مسار أرشيف = https://web.archive.org/web/20160316175639/http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf | تاريخ أرشيف = 16 مارس 2016 }}</ref>
||[[ملف:Parabola animada.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math> {P}_{\,2} </math>
||<math>\ln(1 + \sqrt2) + \sqrt2 \; = \; \operatorname{arcsinh}(1)+\sqrt{2}</math>
||<syntaxhighlight lang="mathematica">ln(1+sqrt 2)+sqrt 2</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A103710}}
||[2;3,2,1,1,1,1,3,3,1,1,4,2,3,2,7,1,6,1,8,7,2,1,...]
||
||<small> 2.29558714939263807403429804918949038 </small>
|-

<!------------------------------------------v-------------------------------------------->
|1.78657645936592246345 
||ثابت سيلفرمان<ref>{{استشهاد بكتاب 
|مؤلف= Steven Finch
|عنوان= Series involving Arithmetric Functions
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/arth.pdf
|سنة= 2007
|ناشر= Harvard.edu
|صفحة= 1
| مسار أرشيف = https://web.archive.org/web/20160419152954/http://www.people.fas.harvard.edu/~sfinch/csolve/arth.pdf | تاريخ أرشيف = 19 أبريل 2016 }}</ref>
||<br /><br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>{\mathcal{S}_{_{m}}}</math>
||<math> \sum_{n = 1}^\infty  \frac {1}{\phi (n)\sigma_1(n)}   = \underset{ p_n: \, {prime}}{ \prod_{n = 1}^\infty \left( 1 + \sum_{k = 1}^\infty  \frac {1}{p_n^{2k} - p_n^{k-1}}\right)}</math> <br /> <div style="text-align: center;"> ''ø''() = [[مؤشر أويلر]]، ''σ''<sub>1</sub>() = [[دالة القواسم]].</div>
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞] 
 {1/[EulerPhi(n) 
 DivisorSigma(1,n)]}</syntaxhighlight>
||
||{{OEIS2C|A093827}} 
||[1;1,3,1,2,5,1,65,11,2,1,2,13,1,4,1,1,1,2,5,4,...]
||
||<small> 1.78657645936592246345859047554131575 </small>
|-

<!--------------------------------------------v------------------------------------------->
|2.59807621135331594029
||مساحة [[سداسي أضلاع|شكل سداسي]] منتظم مع جانب يساوي 1<ref>{{استشهاد بكتاب 
|مؤلف= Nayar
|عنوان= The Steel Handbook
|مسار= https://books.google.com/?id=3QomboYUpVEC&lpg=PA953&dq=2.598076&pg=PA953#v=onepage&q=2.598076&f=false
|سنة= 
|ناشر= Tata McGraw-Hill Education
|صفحة= 953
|مسار أرشيف= https://web.archive.org/web/20200304172917/https://books.google.com/books?id=3QomboYUpVEC&lpg=PA953&dq=2.598076&pg=PA953&hl=en#v=onepage&q=2.598076&f=false|تاريخ أرشيف=2020-03-04}}</ref>
|bgcolor=#ffffff align=center|[[ملف:Esagono.png|80px]]
 |bgcolor=#e0f0f0 align=center|<math>\mathcal{A}_6</math>
||<math> \frac{3 \sqrt{3}}{2} </math>
||<syntaxhighlight lang="mathematica">3 sqrt(3)/2</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A104956}}
||[2;1,1,2,20,2,1,1,4,1,1,2,20,2,1,1,4,1,1,2,20,...] <br /> [2;{{سطر فوقي|1,1,2,20,2,1,1,4}}]
||
||<small> 2.59807621135331594029116951225880855 </small>
|-

<!----------------------------------------v-------------------------------------------->
| 0.66131704946962233528
||ثابت<br /> فيلر تورنر <ref>{{استشهاد بكتاب 
|مؤلف= ECKFORD COHEN
|عنوان= SOME ASYMPTOTIC FORMULAS IN THE THEORY OF NUMBERS
|مسار= http://www.ams.org/journals/tran/1964-112-02/S0002-9947-1964-0166181-5/S0002-9947-1964-0166181-5.pdf
|سنة= 1962
|ناشر= University of Tennessee
|صفحة= 220
| مسار أرشيف = https://web.archive.org/web/20190504110633/https://www.ams.org/journals/tran/1964-112-02/S0002-9947-1964-0166181-5/S0002-9947-1964-0166181-5.pdf | تاريخ أرشيف = 4 مايو 2019 }}</ref>
||<br /><br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>{\mathcal{C}_{_{FT}}}</math>
||<math>\underset{p_n: \, {prime}}{\frac{1}{2}\prod_{n = 1}^\infty \left(1-\frac{2}{p_n^2}\right){+}\frac{1}{2}} =\frac{3}{\pi^2}\prod_{n = 1}^\infty \left(1-\frac{1}{p_n^2-1}\right){+}\frac{1}{2}</math>
||<syntaxhighlight lang="mathematica">[prod[n=1 to ∞] 
 {1-2/prime(n)^2}] 
 /2 + 1/2</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A065493}} 
||[0;1,1,1,20,9,1,2,5,1,2,3,2,3,38,8,1,16,2,2,...]
||1932
||<small> 0.66131704946962233528976584627411853 </small>
|-

<!-----------------------------------------v--------------------------------------------->
| 1.46099848620631835815 
||ثابت باكستر <ref>{{استشهاد بأرخايف 
|author= Paul B. Slater
|title= A Hypergeometric Formula Yielding Hilbert-Schmidt Generic 2 x 2 Generalized Separability Probabilities
|arxiv= 1203.4498
|year= 2013
|class= quant-ph
}}</ref>
|bgcolor=#ffffff align=center| Mapamundi [[ملف:World map with four colours.svg|100px]] Four-Coloring
 |bgcolor=#e0f0f0 align=center|<math>\mathcal{C}^2</math>
||<math> \prod_{n = 1}^\infty \frac{(3n-1)^2}{(3n-2)(3n)}  = \frac {3}{4\pi^2} \,\Gamma \left(\frac {1}{3}\right)^3 </math>
<div style="text-align: center;"> Γ() = [[دالة غاما]] </div>
||<syntaxhighlight lang="mathematica">3×Gamma(1/3) 
 ^3/(4 pi^2)</syntaxhighlight>
||
||{{OEIS2C|A224273}}
||[1;2,5,1,10,8,1,12,3,1,5,3,5,8,2,1,23,1,2,161,...]
||1970
||<small> 1.46099848620631835815887311784605969 </small>
|-

<!-------------------------------------------v-------------------------------------------->
|1.92756197548292530426
||ثابت تترنك
<!---
<ref name="مولد تلقائيا1">{{استشهاد بكتاب 
|عنوان= 
|مسار= 
|سنة= 
}}</ref>
--->
||<br /><br />
|bgcolor=#e0f0f0 align=center|<math>\mathcal{T}</math>
||الجذور الموجبة للمعادلة التالية: <br />
<math> \;\; x^4-x^3-x^2-x-1=0</math>
||<syntaxhighlight lang="mathematica">Root[x+x^-4-2=0]</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A086088}}
||[1;1,12,1,4,7,1,21,1,2,1,4,6,1,10,1,2,2,1,7,1,...]
||
||<small> 1.92756197548292530426190586173662216 </small>
|-

<!----------------------------------------------v---------------------------------------------->
|1.00743475688427937609
||مكعب روبرت الرايني
<!---
<ref name="مولد تلقائيا1" />
--->
||[[ملف:8-cell-orig.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math>{f_{(3,4)}}</math>
||
الجذور الموجبة للمعادلة التالية: <br />
<math> \;\; 4x^4{-}28x^3{-}7x^2{+}16x{+}16=0</math>
||<syntaxhighlight lang="mathematica">Root[4*x^8-28*x^6 
 -7*x^4+16*x^2+16 
 =0]</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A243309}}
||[1;134,1,1,73,3,1,5,2,1,6,3,11,4,1,5,5,1,1,48,...]
||
||<small> 1.00743475688427937609825359523109914 </small>
|-

<!----------------------------------------------v------------------------------------------->
|1.70521114010536776428
||ثابت نيفن <ref>{{استشهاد بكتاب
|مؤلف= Ivan Niven 
|عنوان= Averages of exponents in factoring integers
|مسار= http://www.ams.org/journals/proc/1969-022-02/S0002-9939-1969-0241373-5/S0002-9939-1969-0241373-5.pdf
| مسار أرشيف = https://web.archive.org/web/20190426230138/https://www.ams.org/journals/proc/1969-022-02/S0002-9939-1969-0241373-5/S0002-9939-1969-0241373-5.pdf | تاريخ أرشيف = 26 أبريل 2019 }}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{C}</math>
||<math>1+\sum_{n = 2}^\infty \left(1-\frac{1}{\zeta(n)} \right)</math>
||<syntaxhighlight lang="mathematica">1+ Sum[n=2 to ∞]
{1-(1/Zeta(n))}</syntaxhighlight>
||
||{{OEIS2C|A033150}}
||[1;1,2,2,1,1,4,1,1,3,4,4,8,4,1,1,2,1,1,11,1,...]
||1969
||<small> 1.70521114010536776428855145343450816 </small>
|-

<!---------------------------------------------v------------------------------------------>
| 0.6045997880780726168 
||العلاقة بين مساحة مثلث متساوي الأضلاع والدائر بداخلة
||[[ملف:Fano plane.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math> \frac{\pi}{3 \sqrt 3}</math>
||<br /><math> \sum_{n = 1}^\infty \frac{1}{n{2n \choose n}} =  1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{5} + \frac{1}{7} - \frac{1}{8} + \cdots</math> <div style="text-align: center;"> [[متسلسلة دركليه]] </div>
||<syntaxhighlight lang="mathematica">Sum[1/(n 
Binomial[2 n, n])
, {n, 1, ∞}]</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A073010}}
||[0;1,1,1,1,8,10,2,2,3,3,1,9,2,5,4,1,27,27,6,6,...]
||
||<small> 0.60459978807807261686469275254738524 </small>
|-

<!--------------------------------------------v------------------------------------------->
| 1.15470053837925152901 
|| ثابت [[شارل آرميت|هيرمت]] <ref>{{استشهاد بكتاب
|مؤلف= Steven Finch
|عنوان= Errata and Addenda to Mathematical Constants
|سنة= 2014
|ناشر= Harvard.edu
|isbn= 
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf
| مسار أرشيف = https://web.archive.org/web/20160316175639/http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf | تاريخ أرشيف = 16 مارس 2016 }}</ref>
||
| bgcolor=#e0f0f0 align=center|<math> \gamma_{_{2}} </math>
||<math> \frac{2}{\sqrt{3}} = \frac{1}{\cos \, (\frac{\pi}{6})} </math>
||<syntaxhighlight lang="mathematica">2/sqrt(3)</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||1+<br />{{OEIS2C|A246724}}
||[1;6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] <br /> [1;{{سطر فوقي|6,2}}]
|| 
||<small> 1.15470053837925152901829756100391491 </small>
|-

<!---------------------------------------------v----------------------------------------->
|0.41245403364010759778 
||ثابت موروس <ref>{{استشهاد بكتاب
|مؤلف= Steven Finch
|عنوان= Errata and Addenda to Mathematical Constants
|صفحة= 53
|سنة= 2014
|ناشر= Harvard.edu
|isbn= 
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf
| مسار أرشيف = https://web.archive.org/web/20160316175639/http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf | تاريخ أرشيف = 16 مارس 2016 }}</ref>
||[[ملف:Thue-MorseRecurrence.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math> \tau </math>
||<math> \sum_{n=0}^{\infty} \frac{t_n}{2^{n+1}} </math>  &nbsp;&nbsp; <br />
حيث <math> \tau(x) = \sum_{n=0}^{\infty} (-1)^{t_n} \, x^n  = \prod_{n=0}^{\infty} (1 - x^{2^n} )</math>
||
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A014571}}
||[0;2,2,2,1,4,3,5,2,1,4,2,1,5,44,1,4,1,2,4,1,1,...]
||
||<small> 0.41245403364010759778336136825845528 </small> 
|-

<!--------------------------------------------v---------------------------------------->
|0.58057755820489240229
||ثابت بيل <ref>{{استشهاد بأرخايف 
|author= FRANZ LEMMERMEYER
|title= HIGHER DESCENT ON PELL CONICS. I. FROM LEGENDRE TO SELMER
|arxiv=math/0311309
|year= 2003
}}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{\mathcal{P}_{_{Pell}}}</math>
||<math>1- \prod_{n = 0}^\infty \left(1-\frac{1}{2^{2n+1}}\right) </math>
||<syntaxhighlight lang="mathematica">N[1-prod[n=0 to ∞] 
 {1-1/(2^(2n+1)}]</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A141848}}
||[0;1,1,2,1,1,1,1,14,1,3,1,1,6,9,18,7,1,27,1,1,...]
||
||<small> 0.58057755820489240229004389229702574 </small>
|-

<!----------------------------------------------v-------------------------------------------->
|0.66274341934918158097
||[[نهاية (رياضيات)|نهاية]] [[بيير لابلاس|لابلاس]] <ref>{{استشهاد بكتاب
|مؤلف= Howard Curtis
|عنوان= [[Orbital Mechanics for Engineering Students]]
|صفحة= 159
|سنة= 2014
|ناشر= Elsevier
|isbn= 978-0-08-097747-8
}}</ref>
||[[ملف:Laplace limit.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\lambda}</math>
||<math> \frac{ x \; e^\sqrt{x^2+1}}{\sqrt{x^2+1}+1} = 1</math>
||<syntaxhighlight lang="mathematica">(x e^sqrt(x^2+1))
/(sqrt(x^2+1)+1) = 1</syntaxhighlight>
||
||{{OEIS2C|A033259}}
||[0;1,1,1,27,1,1,1,8,2,154,2,4,1,5,1,1,2,1601,...]
||1782 ~
||<small> 0.66274341934918158097474209710925290 </small>
|-

<!-------------------------------------------v---------------------------------------------->
| 0.17150049314153606586 
||ثابت هال مونتغمري <ref>{{استشهاد بأرخايف
|مؤلف1=Andrew Granville  |مؤلف2=K. Soundararajan
|lastauthoramp=yes |عنوان= The spectrum of multiplicative functions
|سنة= 1999
|arxiv=math/9909190
}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math> {{\delta}_{_{0}}} </math>
|| <math> 1 + \frac{\pi^2}{6} +2 \; \mathrm{Li}_2 \left(-\sqrt{e}\;\right) 
\quad \mathrm{Li}_2 \, \scriptstyle \text{= Dilogarithm integral} </math>
||<syntaxhighlight lang="mathematica">1 + Pi^2/6 + 
2*PolyLog[2, -Sqrt[E]]</syntaxhighlight>
||
||{{OEIS2C|A143301}}
||[0;5,1,4,1,10,1,1,11,18,1,2,19,14,1,51,1,2,1,...]
||
||<small> 0.17150049314153606586043997155521210 </small> 
|-

<!----------------------------------------------v------------------------------------------->
|1.55138752454832039226 
|| مثلث كالبي <ref>{{استشهاد بكتاب
|مؤلف1=John Horton Conway |مؤلف2=Richard K. Guy |عنوان= The Book of Numbers
|صفحة= 242
|سنة= 1995
|ناشر= Copernicus
|isbn= 0-387-97993-X
|مسار= https://books.google.com/?id=0--3rcO7dMYC&lpg=PA206&dq=%22Calabi%20triangle%22&pg=PA206#v=onepage&q=%22Calabi%20triangle%22&f=false
|مسار أرشيف= https://web.archive.org/web/20200304172919/https://books.google.com/books?id=0--3rcO7dMYC&lpg=PA206&dq=%22Calabi+triangle%22&pg=PA206&hl=en#v=onepage&q=%22Calabi%20triangle%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Calabi triangle.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math> {C_{_{CR}}} </math>
|| <math> {1 \over 3} + {(-23 + 3i \sqrt{237})^{\tfrac13} \over 3 \cdot 2^{\tfrac23}} + {11 \over 3 (2 (-23 + 3i \sqrt{237}))^{\tfrac13}} </math>
||<syntaxhighlight lang="mathematica">FindRoot[ 
 2x^3-2x^2-3x+2 
 ==0, {x, 1.5}, 
 WorkingPrecision->40]</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A046095}}
||[1;1,1,4,2,1,2,1,5,2,1,3,1,1,390,1,1,2,11,6,2,...]
||1946 ~
||<small> 1.55138752454832039226195251026462381 </small> 
|-

<!------------------------------------------v--------------------------------------------->
|1.22541670246517764512
||[[غاما]](3/4) <ref>{{استشهاد بكتاب
|مؤلف= John Derbyshire
|عنوان= Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
|صفحة= 147
|سنة= 2003
|ناشر= Joseph Henry Press
|isbn= 0-309-08549-7
|مسار= https://books.google.com/?id=qsoqLNQUIJMC&lpg=PA147&dq=1.2254167024&pg=PA147#v=onepage&q=1.2254167024&f=false
|مسار أرشيف= https://web.archive.org/web/20200304172923/https://books.google.com/?id=qsoqLNQUIJMC&lpg=PA147&dq=1.2254167024&pg=PA147#v=onepage&q=1.2254167024&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>\Gamma(\tfrac34)</math>
||<math>\left(-1+\frac{3}{4}\right)! = \left(-\frac{1}{4}\right)!</math>
||<syntaxhighlight lang="mathematica">(-1+3/4)!</syntaxhighlight>
||
||{{OEIS2C|A068465}}
||[1;4,2,3,2,2,1,1,1,2,1,4,7,1,171,3,2,3,1,1,8,3,...]
||
||<small> 1.22541670246517764512909830336289053 </small>
|-

<!------------------------------------------v---------------------------------------------->
|1.20205690315959428539 
||[[ثابتة أبيري|ثابت أبيري]] <ref>{{استشهاد بكتاب 
|مؤلف1=Annie Cuyt |مؤلف2=Vigdis Brevik Petersen |مؤلف3=Brigitte Verdonk |مؤلف4=Haakon Waadelantl |مؤلف5=William B. Jones. |عنوان= Handbook of Continued Fractions for Special Functions
|مسار= https://books.google.com/?id=DQtpJaEs4NIC&lpg=PA188&dq=1.202056903159594285399738&pg=PA188#v=onepage&q=1.202056903159594285399738&f=false
|سنة= 2008
|ناشر= Springer
|isbn= 978-1-4020-6948-2
|صفحة= 188
|مسار أرشيف= https://web.archive.org/web/20200304172925/https://books.google.com/?id=DQtpJaEs4NIC&lpg=PA188&dq=1.202056903159594285399738&pg=PA188#v=onepage&q=1.202056903159594285399738&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Apéry's constant.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>\zeta(3)</math>
||<math>\sum_{n=1}^\infty\frac{1}{n^3} = \frac{1}{1^3}+\frac{1}{2^3} + \frac{1}{3^3} + \frac{1}{4^3} + \frac{1}{5^3} + \cdots= </math>
<math>\frac{1}{2} \sum_{n=1}^\infty \frac{H_n}{n^2} =
\frac{1}{2} \sum_{i=1}^\infty \sum_{j=1}^\infty \frac{1}{ij(i{+}j)}=
\!\!\int \limits_0^1 \!\!\int \limits_0^1 \!\!\int \limits_0^1 \frac{\mathrm{d}x \mathrm{d}y \mathrm{d}z}{1 - xyz} </math>
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞]
{1/n^3}</syntaxhighlight>
|'''[[عدد غير كسري|غ.ك]]'''
||{{OEIS2C|A010774}}
||[1;4,1,18,1,1,1,4,1,9,9,2,1,1,1,2,7,1,1,7,11,...]
||1979
||<small> 1.20205690315959428539973816151144999 </small>
|-

<!----------------------------------------------v--------------------------------------->
| 0.91596559417721901505 
||[[ثابتة كاتالان|ثابت كاتالان]]<ref>{{استشهاد بكتاب 
|مؤلف= Henri Cohen
|عنوان= Number Theory: Volume II: Analytic and Modern Tools
|مسار= https://books.google.com/?id=5Lp-tGZR25sC&pg=PA127&dq=0.91596559417721901505460351493238411#v=onepage&q=0.91596559417721901505460351493238411&f=false 
|سنة= 2000
|ناشر= Springer
|isbn= 978-0-387-49893-5
|صفحة= 127
|مسار أرشيف= https://web.archive.org/web/20200304172928/https://books.google.com/?id=5Lp-tGZR25sC&pg=PA127&dq=0.91596559417721901505460351493238411#v=onepage&q=0.91596559417721901505460351493238411&f=false|تاريخ أرشيف=2020-03-04}}</ref><ref>{{استشهاد بكتاب 
|مؤلف1=H. M. Srivastava |مؤلف2=Choi Junesang |عنوان= Series Associated With the Zeta and Related Functions
|مسار= https://books.google.com/?id=NBcSzUlaWWAC&pg=PA29&dq=0.915965594177219015#v=onepage&q=0.915965594177219015&f=false
|سنة= 2001
|ناشر= Kluwer Academic Publishers
|isbn= 0-7923-7054-6
|صفحة= 30
|مسار أرشيف= https://web.archive.org/web/20200304172930/https://books.google.com/?id=NBcSzUlaWWAC&pg=PA29&dq=0.915965594177219015#v=onepage&q=0.915965594177219015&f=false|تاريخ أرشيف=2020-03-04}}</ref><ref>{{استشهاد بكتاب
|مؤلف= E. Catalan
|عنوان= Mémoire sur la transformation des séries, et sur quelques intégrales définies, Comptes rendus hebdomadaires des séances de l’Académie des sciences 59
|مسار= https://books.google.de/?id=LXZFAAAAcAAJ&pg=PA618
|سنة= 1864
|ناشر= Kluwer Academic éditeurs
|صفحة= 618
|مسار أرشيف= https://web.archive.org/web/20200304172932/https://books.google.de/?id=LXZFAAAAcAAJ&pg=PA618|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{C}</math>
|| <math> \int_0^1 \!\! \int_0^1 \!\! \frac{1}{1{+}x^2 y^2}\, dx \,dy
= \! \sum_{n = 0}^\infty \! \frac{(-1)^n}{(2n{+}1)^2} \!
= \! \frac{1}{1^2}{-}\frac{1}{3^2}{+}{\cdots} </math>
||<syntaxhighlight lang="mathematica">Sum[n=0 to ∞]
{(-1)^n/(2n+1)^2}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A006752}}
||[0;1,10,1,8,1,88,4,1,1,7,22,1,2,3,26,1,11,...]
||1864
||<small> 0.91596559417721901505460351493238411 </small>
|-

<!-------------------------------------------v------------------------------------------->
|0.78539816339744830961 
||بيتا(1) <ref>{{استشهاد بكتاب
|مؤلف=  Lennart Råde,Bertil 
|عنوان= Mathematics Handbook for Science and Engineering
|صفحة= 423
|سنة= 2000
|ناشر= Springer-Verlag
|isbn= 3-540-21141-1
|مسار= https://books.google.com/?id=zHEjWAgv7joC&lpg=PA423&dq=0.785398163&pg=PA423#v=onepage&q=0.785398163&f=false
|مسار أرشيف= https://web.archive.org/web/20200304172935/https://books.google.com/?id=zHEjWAgv7joC&lpg=PA423&dq=0.785398163&pg=PA423#v=onepage&q=0.785398163&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Loglogisticcdf.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\beta}(1)</math>
||<math>\frac{\pi}{4} = \sum_{n = 0}^\infty \frac{(-1)^n}{2n+1} = \frac{1}{1} - \frac{1}{3} + \frac{1}{5} - \frac{1}{7} + \frac{1}{9} - \cdots</math>
||<syntaxhighlight lang="mathematica">Sum[n=0 to ∞]
{(-1)^n/(2n+1)}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A003881}}
||[0; 1,3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...]
||1805 <br /> to <br /> 1859
||<small> 0.78539816339744830961566084581987572 </small> 
|-

<!-------------------------------------------v----------------------------------------->
|0.001317641154853178109 
||ثابت روجر هيث براون<ref>{{استشهاد بكتاب 
|مؤلف= J. B. Friedlander, A. Perelli, C. Viola, D.R. Heath-Brown, H.Iwaniec, J. Kaczorowski
|عنوان= Analytic Number Theory
|مسار= https://books.google.com/?id=NuDimaRIVVsC&lpg=PA29&dq=%22Heath-Brown%20and%20Moroz%22&pg=PA29#v=onepage&q=%22Heath-Brown%20and%20Moroz%22&f=false
|سنة= 2002
|ناشر= Springer
|isbn= 978-3-540-36363-7 
|صفحة= 29
|مسار أرشيف= https://web.archive.org/web/20200304172937/https://books.google.com/?id=NuDimaRIVVsC&lpg=PA29&dq=%22Heath-Brown%20and%20Moroz%22&pg=PA29#v=onepage&q=%22Heath-Brown%20and%20Moroz%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{C_{_{HBM}}}</math>
||<math>\underset{p_n: \, {prime}}{\prod_{n = 1}^\infty \left(1-\frac{1}{p_n}\right)^7\left(1+\frac{7p_n+1}{p_n^2}\right)} </math>
||<syntaxhighlight lang="mathematica">N[prod[n=1 to ∞] 
 {((1-1/prime(n))^7) 
 *(1+(7*prime(n)+1) 
 /(prime(n)^2))}]</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A118228}}
||[0;758,1,13,1,2,3,56,8,1,1,1,1,1,143,1,1,1,2,...]
||
||<small> 0.00131764115485317810981735232251358 </small>
|-

<!-------------------------------------------v------------------------------------------->
|0.56755516330695782538
||[[فضاء حلقي|الوحدة النمطية]] للرفع [[وحدة تخيلية|الوحدة التخيلية]]''i''
||
| bgcolor=#e0f0f0 align=center|<math>|{}^\infty {i} | </math>
||<math> \lim_{n \to \infty} \left | {}^n i \right |  =\left | \lim_{n \to \infty}  \underbrace{i^{i^{\cdot^{\cdot^{i}}}}}_n  \right |</math>
||<syntaxhighlight lang="mathematica">Mod(i^i^i^...)</syntaxhighlight>
||
||{{OEIS2C|A212479}}
||[0;1,1,3,4,1,58,12,1,51,1,4,12,1,1,2,2,3,...]
||
||<small> 0.56755516330695782538461314419245334 </small>
|-

<!--------------------------------------------v----------------------------------------->
|0.78343051071213440705
||[[حلم الطالب الجامعي]] (1) <br /> ل[[يوهان برنولي|يوهان بيرنولي]] <ref>{{استشهاد بكتاب 
|مؤلف= William Dunham
|عنوان= The Calculus Gallery: Masterpieces from Newton to Lebesgue
|مسار= https://books.google.com/?id=QnXSqvTiEjYC&pg=PA51&lpg=PA51&dq=0.7834305107#v=onepage&q=0.7834305107&f=false
|سنة= 2005 
|ناشر= Princeton University Press
|isbn= 978-0-691-09565-3
|صفحة= 51
|مسار أرشيف= https://web.archive.org/web/20200304172939/https://books.google.com/?id=QnXSqvTiEjYC&pg=PA51&lpg=PA51&dq=0.7834305107#v=onepage&q=0.7834305107&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Reve etudiant.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>{I}_{1}</math>
||<math>\int_0^1 \! x^{x}\,dx = \sum_{n = 1}^\infty \frac{(-1)^{n+1}}{n^n} = \frac{1}{1^1} - \frac{1}{2^2} + \frac{1}{3^3} - {\cdots} </math>
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞] 
 {-(-1)^n /n^n}</syntaxhighlight>
||
||{{OEIS2C|A083648}}
||[0;1,3,1,1,1,1,1,1,2,4,7,2,1,2,1,1,1,2,1,14,...]
||1697
||<small> 0.78343051071213440705926438652697546 </small>
|-

<!-------------------------------------------v------------------------------------------->
|1.291285997062663540407 
||[[حلم الطالب الجامعي]] (2) <br /> ل[[يوهان برنولي|يوهان بيرنولي]] <ref>{{استشهاد بكتاب 
|مؤلف= Jean Jacquelin
|عنوان= SOPHOMORE'S DREAM FUNCTION
|مسار= http://math.eretrandre.org/tetrationforum/attachment.php?aid=788
|سنة= 2010
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20180930065327/http://math.eretrandre.org/tetrationforum/attachment.php?aid=788 | تاريخ أرشيف = 30 سبتمبر 2018 }}</ref>
||[[ملف:Socd 001.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{I}_{2}</math>
||<math> \int_0^1 \! \frac{1}{x^x}\, dx 
= \sum_{n = 1}^\infty \frac{1}{n^n} =  \frac{1}{1^1} + \frac{1}{2^2} + \frac{1}{3^3}  + \frac{1}{4^4}+ \cdots</math>
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞] 
 {1/(n^n)}</syntaxhighlight>
||
||{{OEIS2C|A073009}}
||[1;3,2,3,4,3,1,2,1,1,6,7,2,5,3,1,2,1,8,1,2,4,...]
||1697
||<small> 1.29128599706266354040728259059560054 </small>
|-

<!-----------------------------------------v------------------------------------------->
|0.70523017179180096514 
|| ثابت بريموريال <ref>{{استشهاد بكتاب 
|مؤلف= Simon Plouffe
|عنوان= Sum of the product of inverse of primes
|مسار= http://www.plouffe.fr/simon/constants/primeprod.txt
| مسار أرشيف = https://web.archive.org/web/20170727112901/http://plouffe.fr/simon/constants/primeprod.txt | تاريخ أرشيف = 27 يوليو 2017 }}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{P_\#}</math>
||<math> \underset{ p_n: \, {prime}}{\sum_{n = 1}^\infty \frac{1}{p_n\#} =  \frac{1}{2} + \frac{1}{6} + \frac{1}{30} + \frac{1}{210} + ... = \sum_{k = 1}^\infty \prod_{n = 1}^k \frac {1}{p_n}}   </math>
||<syntaxhighlight lang="mathematica">Sum[k=1 to ∞] 
 (prod[n=1 to k] 
  {1/prime(n)})</syntaxhighlight>
|'''[[عدد غير كسري|غ.ك]]'''
||{{OEIS2C|A064648}}
||[0;1,2,2,1,1,4,1,2,1,1,6,13,1,4,1,16,6,1,1,4,...]
||
||<small> 0.70523017179180096514743168288824851 </small>
|-

<!-----------------------------------------v------------------------------------------->
|0.14758361765043327417
||صيغة بيلي-بوروين-بلوف <ref>{{استشهاد بكتاب 
|مؤلف= Simon Plouffe
|عنوان= The Computation of Certain Numbers Using a Ruler and Compass
|مسار= https://cs.uwaterloo.ca/journals/JIS/compass.html
|صفحة= Vol. 1 (1998), Article 98.1.3
|سنة= 1998
|ناشر= Université du Québec à Montréal
| مسار أرشيف = https://web.archive.org/web/20190914125453/https://cs.uwaterloo.ca/journals/JIS/compass.html | تاريخ أرشيف = 14 سبتمبر 2019 }}</ref>
||[[ملف:Trigo-arctan-animation.gif|100px]]
| bgcolor=#e0f0f0 align=center|<math>{{C}}</math>
||<math> \frac{1}{\pi} \arctan {\frac{1}{2}} 
= \frac{1}{\pi}\sum_{n=0}^\infty \frac {(-1)^n}{(2^{2n+1})(2n+1)}
</math><br /><math>
= \frac{1}{\pi} \left( \frac {1}{2} - \frac {1}{3 \cdot 2^3} +\frac {1}{5 \cdot 2^5} -\frac {1}{7 \cdot 2^7} +\cdots 
\right)</math>
||<syntaxhighlight lang="mathematica">Arctan(1/2)/pi</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A086203}}
||[0;6,1,3,2,5,1,6,5,3,1,1,2,1,1,2,3,1,2,3,2,2,...]
||
||<small> 0.14758361765043327417540107622474052 </small>
|-

<!------------------------------------------v------------------------------------------>
|0.15915494309189533576
||ثابت بلوف <ref>{{استشهاد بكتاب 
|مؤلف= John Srdjan Petrovic
|عنوان= Advanced Calculus: Theory and Practice
|مسار= https://books.google.com/?id=oUfBAQAAQBAJ&lpg=PA65&dq=0.1591549430&pg=PA65#v=onepage&q=0.1591549430&f=false 
|صفحة= 65
|ناشر= CRC Press
|سنة= 2014
|isbn= 978-1-4665-6563-0
|مسار أرشيف= https://web.archive.org/web/20200304172944/https://books.google.com/?id=oUfBAQAAQBAJ&lpg=PA65&dq=0.1591549430&pg=PA65#v=onepage&q=0.1591549430&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{A}</math>
||<math> \frac{1}{2 \pi} </math>
||<syntaxhighlight lang="mathematica">1/(2 pi)</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A086201}}
||[0;6,3,1,1,7,2,146,3,6,1,1,2,7,5,5,1,4,1,2,42,...]
||
||<small> 0.15915494309189533576888376337251436 </small>
|-

<!-----------------------------------------v------------------------------------------->
| 0.29156090403081878013
||ثابت ديمر ثنائي الأبعاد 2D, <br /> <ref>{{استشهاد بأرخايف 
|author= Steven R. Finch
|title= Several Constants Arising in Statistical Mechanics
|arxiv=math/9810155
|year= 1999
}}</ref><ref>{{استشهاد بكتاب 
|مؤلف1=Federico Ardila |مؤلف2=Richard Stanley |عنوان= Several Constants Arising in Statistical Mechanics
|مسار= http://math.sfsu.edu/federico/Articles/teselaciones.pdf
|ناشر= Department of Mathematics, MIT, Cambridge 
| مسار أرشيف = https://web.archive.org/web/20181123141116/http://math.sfsu.edu/federico/Articles/teselaciones.pdf | تاريخ أرشيف = 23 نوفمبر 2018 }}</ref>
||[[ملف:Dominoes tiling 8x8.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\frac{C}{\pi}}</math>
C= [[ثابتة كاتالان|ثابت كاتالان]]
||<math> \int\limits_{-\pi}^{\pi} \frac{\cosh^{-1}\left(\frac{\sqrt{\cos(t)+3}}{\sqrt2}\right)}{4\pi}\,dt </math>
||<syntaxhighlight lang="mathematica">N[int[-pi to pi]
{arccosh(sqrt(
cos(t)+3)/sqrt(2))
/(4*Pi)dt}]</syntaxhighlight>
||
||{{OEIS2C|A143233}}
||[0;3,2,3,16,8,10,3,1,1,2,1,3,1,2,13,1,1,4,1,5,...]
||
||<small> 0.29156090403081878013838445646839491 </small>
|-

<!--------------------------------------------v----------------------------------------->
| 0.498015668118356042<br />
0.15494982830181068512 ''i'' 
||[[عاملي|المضروب]] (''i'')<ref>{{استشهاد بكتاب 
|مؤلف= Andrija S. Radovic
|عنوان= A REPRESENTATION OF FACTORIAL FUNCTION, THE NATURE OF CONSTAT AND A WAY FOR SOLVING OF FUNCTIONAL EQUATION F(x) = x . F(x - 1)
|مسار= https://www.andrijar.com/gamma/gammae.pdf
| مسار أرشيف = https://web.archive.org/web/20101231055424/http://andrijar.com/gamma/gammae.pdf | تاريخ أرشيف = 31 ديسمبر 2010 }}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{i}\,!</math>
||<math> \Gamma (1+i) = i \, \Gamma (i) = \int\limits_0^\infty \frac{t^i}{e^t} \mathrm{d} t</math>
||<syntaxhighlight lang="mathematica">Integral_0^∞ 
 t^i/e^t dt</syntaxhighlight>
|'''[[عدد مركب|خ]]'''
||{{OEIS2C|A212877}} <br /> {{OEIS2C|A212878}}
||[0;6,2,4,1,8,1,46,2,2,3,5,1,10,7,5,1,7,2,...] <br /> - [0;2,125,2,18,1,2,1,1,19,1,1,1,2,3,34,...] ''i''
||
||<small> 0.49801566811835604271369111746219809 <br /> - 0.15494982830181068512495513048388 ''i'' </small>
|-

<!-----------------------------------------v-------------------------------------------->
|2.09455148154232659148 
||ثابت [[جون واليس|واليس]]
||[[ملف:Wallis's Constant.png|100px]]
| bgcolor=#e0f0f0 align=center|<math> W </math>
||<math> \sqrt[3]{\frac{45-\sqrt{1929}}{18}}+\sqrt[3]{\frac{45+\sqrt{1929}}{18}}</math>
||<syntaxhighlight lang="mathematica">(((45-sqrt(1929)) 
 /18))^(1/3)+ 
 (((45+sqrt(1929)) 
 /18))^(1/3)</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A007493}}
||[2;10,1,1,2,1,3,1,1,12,3,5,1,1,2,1,6,1,11,4,...]
||1616 <br /> to <br /> 1703
||<small> 2.09455148154232659148238654057930296 </small>
|-

<!-----------------------------------------v------------------------------------------->
| 0.723648402298200009408
||ثابت سرناك
||
| bgcolor=#e0f0f0 align=center|<math>{C_{sa} }</math>
||<math> \prod_{p>2} \Big(1 - \frac{p+2}{p^3}\Big) </math>
||<syntaxhighlight lang="mathematica">N[prod[k=2 to ∞] 
 {1-(prime(k)+2) 
 /(prime(k)^3)}]</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A065476}}
||[0;1,2,1,1,1,1,1,1,1,4,4,1,1,1,1,1,1,1,8,2,1,1,...]
||
||<small> 0.72364840229820000940884914980912759 </small>
|-

<!----------------------------------------v-------------------------------------------->
| 0.632120558828557678404
||[[ثابت زمني|الثابت الزمني]] <ref>{{استشهاد بكتاب 
|مؤلف1=Kunihiko Kaneko |مؤلف2=Ichiro Tsuda |عنوان= Complex Systems: Chaos and Beyond 
|مسار= https://books.google.com/?id=7lcINfgupggC&lpg=PA211&dq=0.63212&pg=PA208#v=onepage&q=0.63212&f=false
|isbn= 3-540-67202-8
|صفحة= 211
|سنة= 1997
|مسار أرشيف= https://web.archive.org/web/20200614120826/https://books.google.com/books?id=7lcINfgupggC&lpg=PA211&dq=0.63212&pg=PA208&hl=fr#v=onepage&q=0.63212&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Seq1.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\tau}</math>
||<math>  \lim_{n \to \infty} 1-\frac {!n}{n!}=\lim_{n \to \infty} P(n)= \int_{0}^{1}e^{-x}dx = 1{-}\frac{1}{e} = </math> <br />
<math> \sum \limits_{n=1}^{\infty} \frac{(-1)^{n+1}}{n!} =
\frac{1}{1!}{-}\frac{1}{2!}{+}\frac{1}{3!}{-}\frac{1}{4!}{+}\frac{1}{5!}{-}\frac{1}{6!}{+}\cdots </math>
||<syntaxhighlight lang="mathematica">lim_(n->∞) (1- !n/n!) 
 !n=subfactorial</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A068996}}
||[0;1,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] <br /> = [0;1,{{سطر فوقي|1,1,2n}}], n∈ℕ 
||
||<small> 0.63212055882855767840447622983853913 </small>
|-

<!-------------------------------------------v------------------------------------------>
|1.04633506677050318098
||ثابت مينكوفسكي-سيجل <ref>{{استشهاد بكتاب 
|مؤلف= Steven Finch
|عنوان= Minkowski-Siegel Mass Constants
|صفحة= 5
|سنة= 2005
|ناشر= Harvard University
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/ms.pdf
| مسار أرشيف = https://web.archive.org/web/20160419150454/http://www.people.fas.harvard.edu/~sfinch/csolve/ms.pdf | تاريخ أرشيف = 19 أبريل 2016 }}</ref> 
||
| bgcolor=#e0f0f0 align=center|<math> F_1 </math>
||<math> \prod_{n=1}^{\infty} \frac{n!}{\sqrt{2\pi n}\left(\frac{n}{e}\right)^n \sqrt[12]{1+\tfrac1{n}}}</math>
||<syntaxhighlight lang="mathematica">N[prod[n=1 to ∞] 
 n! /(sqrt(2*Pi*n) 
 *(n/e)^n *(1+1/n) 
 ^(1/12))]</syntaxhighlight>
||
||{{OEIS2C|A213080}}
||[1;21,1,1,2,1,1,4,2,1,5,7,2,1,20,1,1,1134,3,..]
||1867 <br /> 1885 <br /> 1935
||<small> 1.04633506677050318098095065697776037 </small>
|-

<!------------------------------------------v------------------------------------------->
|5.244115108584239620929 
||ثابت ليمنيسكيت <ref>{{استشهاد بكتاب 
|عنوان= Evaluation of the complete elliptic integrals by the agm method 
|مسار= http://www2.mae.ufl.edu/~uhk/AGM-2012.pdf
|isbn= 
|ناشر=University of Florida, Department of Mechanical and Aerospace Engineering
|سنة=
| مسار أرشيف = https://web.archive.org/web/20160304085118/http://www2.mae.ufl.edu/~uhk/AGM-2012.pdf | تاريخ أرشيف = 4 مارس 2016 }}</ref>
||<div style="text-align: center;">[[ملف:Lemniscate of Bernoulli.gif|80px]]</div>
| bgcolor=#e0f0f0 align=center|<math>2\varpi</math>
||<math>\frac{[\Gamma(\tfrac14)]^2}{\sqrt{2 \pi}} = 
4\int^1_0 \frac{dx}{\sqrt{(1-x^2)(2-x^2)}} </math>
||<syntaxhighlight lang="mathematica">Gamma[ 1/4 ]^2 
 /Sqrt[ 2 Pi ]</syntaxhighlight>
||
|{{OEIS2C|A064853}}
||[5;4,10,2,1,2,3,29,4,1,2,1,2,1,2,1,4,9,1,4,1,2,...]
||1718
||<small> 5.24411510858423962092967917978223883 </small>
|-

<!--------------------------------------------v----------------------------------------->
|0.661707182267176235155 
||ثابت روبين <ref>{{استشهاد بكتاب
|مؤلف= Steven R. Finch
|عنوان= Mathematical Constants
|صفحة= 479
|سنة= 2003
|ناشر= Cambridge University Press
|isbn= 3-540-67695-3
|مسار= https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA556&dq=Goh-Schmutz#v=onepage&q=Schmutz&f=false
|مسار أرشيف= https://web.archive.org/web/20200304172820/https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA556&dq=Goh-Schmutz#v=onepage&q=Schmutz&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\Delta(3)</math>
||<math> \frac{4 \! + \! 17\sqrt2 \! -6 \sqrt3 \! -7\pi}{105} \! + \! \frac{\ln(1 \! + \! \sqrt2)}{5} \! + \! \frac{2\ln(2 \! + \! \sqrt3)}{5} </math>
||<syntaxhighlight lang="mathematica">(4+17*2^(1/2)-6 
 *3^(1/2)+21*ln(1+ 
 2^(1/2))+42*ln(2+ 
 3^(1/2))-7*Pi)/105</syntaxhighlight>
|
||{{OEIS2C|A073012}}
||[0;1,1,1,21,1,2,1,4,10,1,2,2,1,3,11,1,331,1,4,...]
||1978
||<small> 0.66170718226717623515583113324841358 </small>
|-

<!---------------------------------------v---------------------------------------------->
|1.30357726903429639125 
||ثابت كونواي <ref>{{استشهاد بكتاب 
|مؤلف= Facts On File, Incorporated
|عنوان= Mathematics Frontiers
|مسار= https://books.google.com/?id=gmCSpNhXMooC&lpg=PA45&dq=Conway%20Constant&pg=PA45#v=onepage&q=Conway%20Constant&f=false
|isbn= 978-0-8160-5427-5
|صفحة= 46
|سنة= 1997
|مسار أرشيف= https://web.archive.org/web/20200304172823/https://books.google.com/?id=gmCSpNhXMooC&lpg=PA45&dq=Conway%20Constant&pg=PA45#v=onepage&q=Conway%20Constant&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Conway constant.png|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\lambda}</math>
||<math> \begin{smallmatrix}
x^{71}\quad\ -x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\
-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\
+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\
-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\
-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}\quad\ -7x^{21}+9x^{20}\\
+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\
+5x^{9}+x^{7}\quad\ -7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0 \quad\quad\quad
\end{smallmatrix}</math>
||
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A014715}}
||[1;3,3,2,2,54,5,2,1,16,1,30,1,1,1,2,2,1,14,1,...]
||1987
||<small> 1.30357726903429639125709911215255189 </small>
|-

<!-------------------------------------------v------------------------------------------>
|1.18656911041562545282
||ثابت ليفي<ref>{{استشهاد بكتاب 
|مؤلف= Aleksandr I͡Akovlevich Khinchin
|عنوان= Continued Fractions
|مسار= https://books.google.com/?id=R7Fp8vytgeAC&pg=PA66
|isbn= 978-0-486-69630-0
|ناشر= Courier Dover Publications 
|صفحة= 66
|سنة= 1997
|مسار أرشيف= https://web.archive.org/web/20200304172826/https://books.google.com/books?id=R7Fp8vytgeAC&pg=PA66&hl=en|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>{\beta}</math>
||<math>\frac {\pi^2}{12\,\ln 2}</math>
||<syntaxhighlight lang="mathematica">pi^2 /(12 ln 2)</syntaxhighlight>
||
||{{OEIS2C|A100199}}
||[1;5,2,1,3,1,1,28,18,16,3,2,6,2,6,1,1,5,5,9,...]
||1935
||<small> 1.18656911041562545282172297594723712 </small>
|-

<!------------------------------------------v------------------------------------------->
|0.83564884826472105333
||[[مبرهنة باكر]] <ref>{{استشهاد بكتاب
|مؤلف= Jean-Pierre Serre
|عنوان= Travaux de Baker
|صفحة= 74
|سنة= 1969–1970
|ناشر= NUMDAM, Séminaire N. Bourbaki.
|مسار= http://archive.numdam.org/ARCHIVE/SB/SB_1969-1970__12_/SB_1969-1970__12__73_0/SB_1969-1970__12__73_0.pdf| مسار أرشيف = https://web.archive.org/web/20121014235439/http://archive.numdam.org/ARCHIVE/SB/SB_1969-1970__12_/SB_1969-1970__12__73_0/SB_1969-1970__12__73_0.pdf | تاريخ أرشيف = 14 أكتوبر 2012 }}</ref>
||[[ملف:Baker constant.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>\beta_3</math>
||<math>\int^1_0 \frac{{\mathrm{d} t}}{1 + t^3}=\sum_{n = 0}^\infty \frac{(-1)^n}{3n+1}= \frac{1}{3}\left(\ln 2+\frac{\pi}{\sqrt{3}}\right)</math>
||<syntaxhighlight lang="mathematica">Sum[n=0 to ∞] 
 {((-1)^(n))/(3n+1)}</syntaxhighlight>
||
||{{OEIS2C|A113476}}
||[0;1,5,11,1,4,1,6,1,4,1,1,1,2,1,3,2,2,2,2,1,3,...]
||
||<small> 0.83564884826472105333710345970011076 </small>
|-

<!------------------------------------------v------------------------------------------->
|23.10344790942054161603
||متتالية كيمبنر(0) <ref>{{استشهاد بكتاب
|مؤلف= Julian Havil
|عنوان= Gamma: Exploring Euler's Constant
|مسار= https://books.google.com/?id=7-sDtIy8MNIC&lpg=PA31&dq=Gamma%3A%20Exploring%20Euler's%20Constant%2C%20Julian%20Havil%2C%20Kempner&pg=PA31#v=onepage&q=Gamma:%20Exploring%20Euler's%20Constant,%20Julian%20Havil,%20Kempner&f=false
|سنة= 2003 
|ناشر= Princeton University Press
|isbn= 9780691141336 
|صفحة= 31
|مسار أرشيف= https://web.archive.org/web/20200304172949/https://books.google.com/?id=7-sDtIy8MNIC&lpg=PA31&dq=Gamma%3A%20Exploring%20Euler's%20Constant%2C%20Julian%20Havil%2C%20Kempner&pg=PA31#v=onepage&q=Gamma:%20Exploring%20Euler's%20Constant,%20Julian%20Havil,%20Kempner&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{K_0}</math>
||<math>1{+}\frac12{+}\frac13{+}\cdots{+}\frac19{+}\frac1{11}{+}\cdots{+}\frac1{19}{+}\frac1{21}{+}\cdots</math>
<math>{+}\frac1{99}{+}\frac1{111}{+}\cdots{+}\frac1{119}{+}\frac1{121}{+}\cdots
</math>

||<syntaxhighlight lang="mathematica">1+1/2+1/3+1/4+1/5
+1/6+1/7+1/8+1/9
+1/11+1/12+1/13
+1/14+1/15+...</syntaxhighlight>
||
||{{OEIS2C|A082839}}
||[23;9,1,2,3244,1,1,5,1,2,2,8,3,1,1,6,1,84,1,...]
||
||<small> 23.1034479094205416160340540433255981 </small>
|-

<!----------------------------------------------v--------------------------------------->
|0.989431273831146951741 
||ثابت ليبسج <ref>{{استشهاد بكتاب 
|مؤلف= Horst Alzer
|عنوان= Journal of Computational and Applied Mathematics, Volume 139, Issue 2
|مسار= http://ac.els-cdn.com/S0377042701004265/1-s2.0-S0377042701004265-main.pdf?_tid=c20cf466-f4bf-11e3-bd9c-00000aacb362&acdnat=1402859198_57de7868bcc50086f092c66898ec6a33
|سنة= 2002
|ناشر= Elsevier
|isbn= 
|صفحات= 215–230 
}}</ref> 
||[[ملف:Fourier synthesis.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math>{C_1}</math>
||<math>\lim_{n\to\infty}\!\! \left(\!{L_n{-}\frac{4}{\pi^2}\ln(2n{+}1)}\!\!\right)\!{=}
\frac{4}{\pi^2}\!\left({\sum_{k=1}^\infty \!\frac{2\ln k}{4k^2{-}1}}
{-}\frac{\Gamma'(\tfrac12)}{\Gamma(\tfrac12)}\!\!\right)</math>
||<syntaxhighlight lang="mathematica">4/pi^2*[(2 
 Sum[k=1 to ∞] 
 {ln(k)/(4*k^2-1)}) 
 -poligamma(1/2)]</syntaxhighlight>
||
||{{OEIS2C|A243277}}
||[0;1,93,1,1,1,1,1,1,1,7,1,12,2,15,1,2,7,2,1,5,...]
||
||<small> 0.98943127383114695174164880901886671 </small>
|-

<!------------------------------------------v------------------------------------------->
|0.19452804946532511361 
||المعامل الثاني لدي بو ريموند <ref>{{استشهاد بكتاب 
|مؤلف= Steven R. Finch 
|عنوان= Mathematical Constants
|مسار=https://archive.org/details/mathematicalcons0000finc
|التسجيل= registration
|سنة= 2003 
|ناشر= Cambridge University Press
|isbn= 3-540-67695-3
|صفحة= [https://archive.org/details/mathematicalcons0000finc/page/238 238]
| مسار أرشيف = https://web.archive.org/web/20210308095707/https://archive.org/details/mathematicalcons0000finc | تاريخ أرشيف = 8 مارس 2021 }}</ref>
||
| bgcolor=#e0f0f0 align=center|<math>{C_2}</math>
||<math>\frac{e^2-7}{2} = \int_0^\infty \left|{\frac{d}{dt}\left(\frac{\sin t}{t}\right)^n}\right|\,dt-1 </math>
||<syntaxhighlight lang="mathematica">(e^2-7)/2</syntaxhighlight> 
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A062546}}
||[0;5,7,9,11,13,15,17,19,21,23,25,27,29,31,...]<br /> = [0;{{سطر فوقي|2p+3}}], p∈ℕ
||
||<small> 0.19452804946532511361521373028750390 </small>
|-

<!--------------------------------------------v----------------------------------------->
|0.78853056591150896106 
||ثابت لورث<ref>{{استشهاد بكتاب 
|مؤلف= Steven Finch
|عنوان= Continued Fraction Transformation III
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/kz3.pdf
|isbn= 
|ناشر= Harvard University
|صفحة= 5
|سنة= 2007
| مسار أرشيف = https://web.archive.org/web/20160419100912/http://www.people.fas.harvard.edu/~sfinch/csolve/kz3.pdf | تاريخ أرشيف = 19 أبريل 2016 }}</ref>
||<div style="text-align: center;">[[ملف:Constante de Lüroth.svg|35px]]</div>
| bgcolor=#e0f0f0 align=center|<math>C_L</math>
||<math>\sum_{n = 2}^\infty \frac{\ln\left(\frac{n}{n-1}\right)}{n}</math>
||<syntaxhighlight lang="mathematica">Sum[n=2 to ∞] 
 log(n/(n-1))/n</syntaxhighlight>
||
|{{OEIS2C|A085361}}
||[0;1,3,1,2,1,2,4,1,127,1,2,2,1,3,8,1,1,2,1,16,...]
||
||<small> 0.78853056591150896106027632216944432 </small>
|-

<!-------------------------------------------v------------------------------------------>
| 1.187452351126501054595
||ثابت غوياس <sub>α</sub> <ref>{{استشهاد بكتاب 
|مؤلف= Andrei Vernescu
|عنوان= Gazeta Matemetica Seria a revista de cultur Matemetica Anul XXV(CIV)Nr. 1, Constante de tip Euler generalízate
|مسار= https://ssmr.ro/gazeta/gma/2007/gma-1-2007.pdf
|سنة= 2007
|صفحة= 14
| مسار أرشيف = https://web.archive.org/web/20181008135422/http://ssmr.ro/gazeta/gma/2007/gma-1-2007.pdf | تاريخ أرشيف = 8 أكتوبر 2018 }}</ref>
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>F_\alpha</math>
||<math> x_{n+1} = \left( 1 + \frac{1}{x_n} \right)^n\text{ for }n=1,2,3,\ldots </math>
||
|
||{{OEIS2C|A085848}}
||[1;5,2,1,81,3,2,2,1,1,1,1,1,6,1,1,3,1,1,4,3,2,...]
||2000
||<small> 1.18745235112650105459548015839651935 </small>
|-

<!------------------------------------------v------------------------------------------->
|2.293166287411861031508
||ثابت غوياس <sub>β</sub> 
||[[ملف:Foias constant.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>F_\beta</math>
||<math> x^{x+1} = (x+1)^x</math>
||<syntaxhighlight lang="mathematica">x^(x+1) 
 = (x+1)^x</syntaxhighlight>
|
||{{OEIS2C|A085846}}
||[2;3,2,2,3,4,2,3,2,130,1,1,1,1,1,6,3,2,1,15,1,...]
||2000
||<small> 2.29316628741186103150802829125080586 </small>
|-

<!--------------------------------------------v----------------------------------------->
|0.82246703342411321823 
||ثابت نيسلون-[[سرينفاسا أينجار رامانجن|رامانجن]] <ref>{{استشهاد بكتاب 
|مؤلف= Mauro Fiorentini
|عنوان= Nielsen – Ramanujan (costanti di)
|مسار= http://bitman.name/math/article/872 
| مسار أرشيف = https://web.archive.org/web/20170220012754/http://bitman.name/math/article/872 | تاريخ أرشيف = 20 فبراير 2017 }}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>\frac{{\zeta}(2)}{2}</math>
||<math> \frac{\pi^2}{12} = \sum_{n=1}^\infty\frac{(-1)^{n+1}}{n^2} = \frac{1}{1^2} {-} \frac{1}{2^2} {+} \frac{1}{3^2} {-} \frac{1}{4^2} {+} \frac{1}{5^2} {-} \cdots </math>
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞]
{((-1)^(n+1))/n^2}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A072691}}
||[0;1,4,1,1,1,2,1,1,1,1,3,2,2,4,1,1,1,1,1,1,4...]
||1909
||<small> 0.82246703342411321823620758332301259 </small>
<!-- 0.90689968211710892529703912882107786<br>sqrt(C) = Pi/(2*sqrt(3)) = {{OEIS2C|A093766}} -->
|-

<!------------------------------------------v------------------------------------------->
|0.69314718055994530941 
||[[لوغاريتم طبيعي|اللوغارتم الطبيعي]] للرقم 2 <ref>{{استشهاد بكتاب 
|مؤلف1=Annie Cuyt |مؤلف2=Vigdis Brevik Petersen |مؤلف3=Brigitte Verdonk |مؤلف4=Haakon Waadeland |مؤلف5=William B. Jones |عنوان= Handbook of Continued Fractions for Special Functions
|مسار= https://books.google.com/?id=DQtpJaEs4NIC&lpg=PA182&dq=0.6931471805599&pg=PA182#v=onepage&q=0.6931471805599&f=false
|سنة= 2008
|ناشر= Springer
|isbn= 978-1-4020-6948-2
|صفحة= 182
|مسار أرشيف= https://web.archive.org/web/20200304172952/https://books.google.com/?id=DQtpJaEs4NIC&lpg=PA182&dq=0.6931471805599&pg=PA182#v=onepage&q=0.6931471805599&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Alternating Harmonic Series.PNG|100px]]
| bgcolor=#e0f0f0 align=center|<math>Ln(2)</math>
||<math> \sum_{n=1}^\infty \frac{1}{n 2^n} = 
\sum_{n=1}^\infty \frac{({-}1)^{n+1}}{n} 
= \frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+{\cdots} </math>
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞]
{(-1)^(n+1)/n}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A002162}}
||[0;1,2,3,1,6,3,1,1,2,1,1,1,1,3,10,1,1,1,2,1,1,...]
||1550 <br /> to <br /> 1617
||<small> 0.69314718055994530941723212145817657 </small>
|-

<!-------------------------------------------v------------------------------------------>
| 0.47494937998792065033 
||ثابت [[كارل فايرشتراس|ويرستراس]] <ref>{{استشهاد بكتاب 
|مؤلف= Eric W. Weisstein
|عنوان= CRC Concise Encyclopedia of Mathematics, Second Edition
|مسار= https://books.google.com/?id=aFDWuZZslUUC&pg=PA3184&dq=%22Weierstrass+Constant%22#v=onepage&q=%22Weierstrass%20Constant%22&f=false
|سنة= 2003 
|ناشر= CRC Press
|isbn= 1-58488-347-2
|صفحة= 151
|مسار أرشيف= https://web.archive.org/web/20200304172954/https://books.google.com/?id=aFDWuZZslUUC&pg=PA3184&dq=%22Weierstrass+Constant%22#v=onepage&q=%22Weierstrass%20Constant%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
| bgcolor=#e0f0f0 align=center|<math>\sigma(\tfrac12)</math>
||<math> \frac{e^{\frac{\pi}{8}}\sqrt{\pi}}{4 \cdot 2^{3/4} {(\frac {1}{4}!)^2}}</math>
||<syntaxhighlight lang="mathematica">(E^(Pi/8) Sqrt[Pi])
 /(4 2^(3/4) (1/4)!^2)</syntaxhighlight>
||
||{{OEIS2C|A094692}}
||[0;2,9,2,11,1,6,1,4,6,3,19,9,217,1,2,4,8,6...]
||1872 
||<small> 0.47494937998792065033250463632798297 </small>
|-

<!------------------------------------------v------------------------------------------->
|0.577215664901532860606
||[[ثابتة أويلر-ماسكيروني|ثابت أويلر-ماسكيروني]]
||[[ملف:Euler-Mas.jpg|100px]]
| bgcolor=#e0f0f0 align=center|<math>{\gamma}</math>
||<math> \sum_{n=1}^\infty \sum_{k=0}^\infty \frac{(-1)^k}{2^n+k} 
 = \sum_{n=1}^\infty \left(\frac{1}{n} -\ln \left(1+\frac{1}{n}\right)\right) </math> <br /> 
<math>= \int_{0}^{1} -\ln \left(\ln \frac{1}{x}\right)\, dx = -\Gamma'(1) = -\Psi(1)</math>
||<syntaxhighlight lang="mathematica">sum[n=1 to ∞]
|sum[k=0 to ∞]
{((-1)^k)/(2^n+k)}</syntaxhighlight>
||
||{{OEIS2C|A001620}}
||[0;1,1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,...]
||1735
||<small> 0.57721566490153286060651209008240243 </small>
<!-- 0.42278433509846713939348790991759757<br> 1 − ''γ'' = {{OEIS2C|A153810}} -->
|-

<!--------------------------------------------v----------------------------------------->
|1.38135644451849779337
||ثابت بيتا كينسر ماهلر ل[[متعددة الحدود]]<ref>{{استشهاد بكتاب 
|مؤلف= P. HABEGGER
|عنوان= MULTIPLICATIVE DEPENDENCE AND ISOLATION I
|صفحة= 2
|سنة= 2003
|ناشر= Institut für Mathematik, Universität Basel, Rheinsprung Basel, Switzerland
|مسار= https://www.math.uni-frankfurt.de/~habegger/multdep1.pdf| مسار أرشيف = https://web.archive.org/web/20160303212006/http://www.math.uni-frankfurt.de/~habegger/multdep1.pdf | تاريخ أرشيف = 3 مارس 2016 }}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\beta</math>
||<math> e^{^{\textstyle{\frac{2}{\pi}} \displaystyle{\int_0^{\frac{\pi}{3}}} \textstyle{t \tan t\ dt}}} = 
         e^{^{\displaystyle{\,\int_{\frac{-1}{3}}^{\frac{1}{3}}} \textstyle{\,\ln \lfloor 1+e^{2 \pi i t}} \rfloor dt}}</math>
||<small> <syntaxhighlight lang="mathematica">e^((PolyGamma(1,4/3) 
 - PolyGamma(1,2/3) 
 +9)/(4*sqrt(3)*Pi))</syntaxhighlight> </small>
|
||{{OEIS2C|A242710}}
||[1;2,1,1,1,1,1,4,1,139,2,1,3,5,16,2,1,1,7,2,1,...]
||1963
||<small> 1.38135644451849779337146695685062412 </small>
|-

<!--------------------------------------------v----------------------------------------->
|1.358456274182988435206
||الدوامة الذهبية 
||[[ملف:FakeRealLogSpiral.svg|100px]]
| bgcolor=#e0f0f0 align=center|<math> c </math>
||<math> \varphi ^ \frac{2}{\pi} = \left(\frac{1 + \sqrt{5}}{2}\right)^{\frac{2}{\pi}}</math>
||<syntaxhighlight lang="mathematica">GoldenRatio^(2/pi)</syntaxhighlight>
||
|{{OEIS2C|A212224}}
||[1;2,1,3,1,3,10,8,1,1,8,1,15,6,1,3,1,1,2,3,1,1,...]
||
||<small> 1.35845627418298843520618060050187945 </small>
<!-- 0.30634896253003312211567570119977068<br>ln(''c'') = (2/{{pi}})ln(''φ'') = {{OEIS2C|A212225}} -->
|-

<!--------------------------------------------v----------------------------------------->
| 0.57595996889294543964 
||[[جداء أويلر|ثابت ستيفين]] <ref>{{استشهاد بكتاب
|مؤلف= Steven Finch
|عنوان= Class Number Theory
|صفحة=8
|سنة= 2005
|ناشر= Harvard University
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/clss.pdf
| مسار أرشيف = https://web.archive.org/web/20160419150530/http://www.people.fas.harvard.edu/~sfinch/csolve/clss.pdf | تاريخ أرشيف = 19 أبريل 2016 }}</ref>
||
| bgcolor=#e0f0f0 align=center|<math> C_S </math>
||<math> \prod_{n = 1}^\infty \left(1 - \frac{p}{p^3-1}\right) </math>
||<syntaxhighlight lang="mathematica">Prod[n=1 to ∞] 
 {1-hprime(n) 
 /(hprime(n)^3-1)}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
|{{OEIS2C|A065478}}
||[0;1,1,2,1,3,1,3,1,2,1,77,2,1,1,10,2,1,1,1,7,...]
||
||<small> 0.57595996889294543964316337549249669 </small>
|-

<!---------------------------------------------v---------------------------------------->
|0.73908513321516064165
||[[نقطة ثابتة (الرياضيات)|عدد دوتي]] <ref>{{استشهاد بكتاب 
|مؤلف= James Stewart
|عنوان= Single Variable Calculus: Concepts and Contexts
|مسار= https://books.google.com/?id=eztUxtCfNXoC&lpg=PP1&dq=Single%20Variable%20Calculus%3A%20Concepts%20and%20Contexts%20%20Escrito%20por%20James%20Stewart&pg=PA314#v=onepage&q=Single%20Variable%20Calculus:%20Concepts%20and%20Contexts%20%20Escrito%20por%20James%20Stewart&f=false
|isbn= 978-0-495-55972-6
|ناشر= Brooks/Cole
|صفحة= 314
|سنة= 2010
|مسار أرشيف= https://web.archive.org/web/20200304172828/https://books.google.com/?id=eztUxtCfNXoC&lpg=PP1&dq=Single%20Variable%20Calculus%3A%20Concepts%20and%20Contexts%20%20Escrito%20por%20James%20Stewart&pg=PA314#v=onepage&q=Single%20Variable%20Calculus:%20Concepts%20and%20Contexts%20%20Escrito%20por%20James%20Stewart&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Dottie number.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>d</math>
||<math> \lim_{x\to \infty} \cos^{[x]}(c) = \lim_{x\to \infty} \underbrace{\cos(\cos(\cos(\cdots(\cos(c)))))}_x</math>
||<syntaxhighlight lang="mathematica">cos(c)=c</syntaxhighlight>
|'''[[عدد متسام|م]]'''
|{{OEIS2C|A003957}}
||[0;1,2,1,4,1,40,1,9,4,2,1,15,2,12,1,21,1,17,...]
||
||<small> 0.73908513321516064165531208767387340 </small>
|-

<!-----------------------------------------v-------------------------------------------->
|0.67823449191739197803
||[[جداء أويلر|ثابت تانيجوتشي]] <ref>{{استشهاد بكتاب
|مؤلف= Steven Finch
|عنوان= Class Number Theory
|صفحة= 8
|سنة= 2005
|ناشر= Harvard University
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/clss.pdf
| مسار أرشيف = https://web.archive.org/web/20160419150530/http://www.people.fas.harvard.edu/~sfinch/csolve/clss.pdf | تاريخ أرشيف = 19 أبريل 2016 }}</ref>
||
|bgcolor=#e0f0f0 align=center|<math> C_T </math>
||<math> \prod_{n = 1}^\infty \left(1 - \frac{3}{{p_n}^3}+\frac{2}{{p_n}^4}+rac{1}{{p_n}^5}-rac{1}{{p_n}^6}
ight) </math>
<div style="text-align: center;"><math>\scriptstyle p_{n}= \, 	ext{prime} </math></div>
||<syntaxhighlight lang="mathematica">Prod[n=1 to ∞] {1 
 -3/ithprime(n)^3 
 +2/ithprime(n)^4 
 +1/ithprime(n)^5 
 -1/ithprime(n)^6}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
|{{OEIS2C|A175639}}
||[0;1,2,9,3,1,2,9,11,1,13,2,15,1,1,1,2,4,1,1,1,...]
||
||<small> 0.67823449191739197803553827948289481 </small>
|-

<!------------------------------------------v------------------------------------------->
|1.85407467730137191843
||ثابت [[كارل فريدريش غاوس|جاووس]] ليمنيسكيت<ref>{{استشهاد بكتاب 
|مؤلف= Steven R. Finch 
|عنوان= Mathematical Constants
|مسار= https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA421&lpg=PA421&dq=Gauss%27+lemniscate+constant#v=onepage&q=Gauss%27%20lemniscate%20constant&f=false
|سنة= 2003 
|ناشر= Cambridge University Press
|isbn= 3-540-67695-3
|صفحة= 421
|مسار أرشيف= https://web.archive.org/web/20200304172830/https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA421&lpg=PA421&dq=Gauss%27+lemniscate+constant#v=onepage&q=Gauss%27%20lemniscate%20constant&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Lemniscate Building.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math> L \text{/}\sqrt{2}</math>
||<math>\int\limits_0^\infty \frac{{\mathrm{d} x}}{\sqrt{1 + x^4}}
 = \frac {1}{4\sqrt{\pi}} \,\Gamma \left(\frac {1}{4}\right)^2
 = \frac{4 \left(\frac {1}{4}!\right)^2} {\sqrt{\pi}}</math>
<div style="text-align: center;"><math>\scriptstyle \Gamma() \text{= Gamma function} </math></div>
||<syntaxhighlight lang="mathematica">pi^(3/2)/(2 Gamma(3/4)^2)</syntaxhighlight>
||
|{{OEIS2C|A093341}}
||[1;1,5,1,5,1,3,1,6,2,1,4,16,3,112,2,1,1,18,1,...]
||
||<small> 1.85407467730137191843385034719526005 </small>
|-

<!------------------------------------------v------------------------------------------->
|1.75874362795118482469
||ثابت الضرب اللانهائي <ref>{{استشهاد بكتاب 
|مؤلف= Steven R. Finch 
|عنوان= Mathematical Constants
|مسار= http://my.safaribooksonline.com/book/math/9781107266582/2-constants-associated-with-number-theory/210_sierpinskis_constant
|سنة= 2003 
|ناشر= Cambridge University Press
|isbn= 3-540-67695-3
|صفحة= 122
|مسار أرشيف= https://web.archive.org/web/20200304172956/http://my.safaribooksonline.com/book/math/9781107266582/2-constants-associated-with-number-theory/210_sierpinskis_constant|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math> Pr_1</math>
||<math> \prod_{n = 2}^\infty \Big(1 + \frac{1}{n}\Big)^\frac{1}{n}</math>
||<syntaxhighlight lang="mathematica">Prod[n=2 to inf] 
{(1+1/n)^(1/n)}</syntaxhighlight>
||
||{{OEIS2C|A242623}}
||[1;1,3,6,1,8,1,4,3,1,4,1,1,1,6,5,2,40,1,387,2,...]
||1977
||<small> 1.75874362795118482469989684865589317 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|1.86002507922119030718
||[[حلزون (هندسة)|حلزون]] [[ثيودورس القوريني|تيودوروس]] <ref>{{استشهاد بكتاب
|مؤلف= Jorg Waldvogel
|عنوان= Analytic Continuation of the Theodorus Spiral
|صفحة=16
|سنة= 2008
|مسار= http://www.sam.math.ethz.ch/~joergw/Papers/theopaper.pdf
| مسار أرشيف = https://web.archive.org/web/20160303182911/http://www.sam.math.ethz.ch/~joergw/Papers/theopaper.pdf | تاريخ أرشيف = 3 مارس 2016 }}</ref> 
||[[ملف:Spiral of Theodorus.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math> \partial </math>
||<math> \sum_{n=1}^{\infty} \frac{1}{\sqrt{n^3} + \sqrt{n}} =
\sum_{n=1}^{\infty} \frac{1}{\sqrt{n} (n+1)}</math>
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞] 
 {1/(n^(3/2) 
 +n^(1/2))}</syntaxhighlight>
||
||{{OEIS2C|A226317}}
||[1;1,6,6,1,15,11,5,1,1,1,1,5,3,3,3,2,1,1,2,19,...]
||-460 <br /> to <br /> -399
||<small> 1.86002507922119030718069591571714332 </small>
|-

<!-------------------------------------------v------------------------------------------>
|2.79128 78474 77920 00329
||متداخلة [[جذر نوني|جذرية]] S<sub>5</sub> 
||
|bgcolor=#e0f0f0 align=center|<math> S_{5} </math>
||<math>\displaystyle \frac{\sqrt{21}+1}{2} =  
\scriptstyle  \, \sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5+\cdots}}}}}\; </math>
<math> = 1+ \, \scriptstyle \sqrt{5-\sqrt{5-\sqrt{5-\sqrt{5-\sqrt{5-\cdots}}}}}\; </math>
||<syntaxhighlight lang="mathematica">(sqrt(21)+1)/2</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||[http://oeis.org/A222134 A222134]
||[2;1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,1,3,...]<br />[2;{{سطر فوقي|1,3}}]
||
||<small> 2.79128784747792000329402359686400424 </small>
|-

<!-------------------------------------------v------------------------------------------>
|0.70710678118654752 br> +0.70710 67811 86547 524 i>
||[[جذر تربيعي|الجذر التربيعي]] [[وحدة تخيلية|للوحدة التخيلية]]''i'' <ref>{{استشهاد بكتاب
|مؤلف1=Robert Kaplan |مؤلف2=Ellen Kaplan |عنوان= The Art of the Infinite: The Pleasures of Mathematics
|سنة= 2014
|صفحة= 238
|ناشر=Oxford University Press/Bloomsburv Press |isbn= 978-1-60819-869-6
|مسار= https://books.google.com/?id=KXdvAAAAQBAJ&lpg=PA238&dq=0.707106781&pg=PA238#v=onepage&q=0.707106781&f=false
|مسار أرشيف= https://web.archive.org/web/20200304172959/https://books.google.com/?id=KXdvAAAAQBAJ&lpg=PA238&dq=0.707106781&pg=PA238#v=onepage&q=0.707106781&f=false|تاريخ أرشيف=2020-03-04}}</ref> 
||[[ملف:Imaginary2Root.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math> \sqrt{i} </math>
||<math> \sqrt[4]{-1} = \frac{1+i}{\sqrt{2}} = e^ \frac{i\pi}{4} =
 \cos\left (\frac{\pi}{4} \right) + i\sin\left (\frac{\pi}{4} \right) </math>
||<syntaxhighlight lang="mathematica">(1+i)/(sqrt 2)</syntaxhighlight>
|'''[[عدد جبري|ج]]'''<br />'''[[عدد مركب|خ]]'''
||{{OEIS2C|A010503}}
||[0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] <br />= [0;1,{{سطر فوقي|2}},...] <br /> [0;1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,..] ''i'' <br />= [0;1,{{سطر فوقي|2}},...] ''i''
||
||<small> 0.70710678118654752440084436210484903 </small> <br/> <small> + 0.70710678118654752440084436210484 ''i'' </small>
|-

<!----------------------------------------------v--------------------------------------->
|0.809394020540639130717
||ثابت اللادي – جرينستيد<ref>{{استشهاد بكتاب 
|مؤلف= Steven R. Finch 
|عنوان= Mathematical Constants
|مسار= https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA121&lpg=PA121&dq=0.8093940205#v=onepage&q=0.8093940205&f=false 
|سنة= 2003 
|ناشر= Cambridge University Press
|isbn= 3-540-67695-3
|صفحة= 121
|مسار أرشيف= https://web.archive.org/web/20200304173001/https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA121&lpg=PA121&dq=0.8093940205#v=onepage&q=0.8093940205&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\mathcal{A}_{AG}}</math>
||<math> e^{-1+\sum \limits_{k=2}^\infty \sum \limits_{n=1}^\infty \frac{1}{n k^{n+1}}} = e^{-1-\sum \limits_{k=2}^\infty \frac{1}{k} \ln \left( 1-\frac{1}{k}\right)} </math>
||<small> <syntaxhighlight lang="mathematica">e^{(sum[k=2 to ∞] 
 |sum[n=1 to ∞] 
 {1/(n k^(n+1))})-1}</syntaxhighlight> </small>
||
||{{OEIS2C|A085291}}
||[0;1,4,4,17,4,3,2,5,3,1,1,1,1,6,1,1,2,1,22,...] 
||1977
||<small> 0.80939402054063913071793188059409131 </small> 
|-

<!----------------------------------------------v--------------------------------------->
|2.58498175957925321706 
||ثابت [[فاتسواف شيربينسكي|شيربينسكي]] <ref>{{استشهاد بكتاب
|مؤلف= Eric W. Weisstein 
|عنوان= CRC Concise Encyclopedia of Mathematics, Second Edition
|صفحة=1356
|سنة= 2002
|ناشر= CRC Press
|مسار= https://books.google.com/?id=aFDWuZZslUUC&pg=PA2685&dq=1.584962500#v=onepage&q=1.584962500&f=false
|isbn= 9781420035223
|مسار أرشيف= https://web.archive.org/web/20200304173003/https://books.google.com/?id=aFDWuZZslUUC&pg=PA2685&dq=1.584962500#v=onepage&q=1.584962500&f=false|تاريخ أرشيف=2020-03-04}}</ref> 
||[[ملف:Random Sierpinski Triangle animation.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math> {K} </math>
||<math>\pi\left(2\gamma+\ln\frac{4\pi^3}{\Gamma(\tfrac{1}{4})^4}\right) =
  \pi (2 \gamma + 4 \ln\Gamma(\tfrac{3}{4}) - \ln\pi) </math>
<math> = \pi \left(2 \ln 2+3 \ln \pi + 2 \gamma - 4 \ln \Gamma (\tfrac{1}{4})\right)</math>
||<syntaxhighlight lang="mathematica">-Pi Log[Pi]+2 Pi 
  EulerGamma
+4 Pi Log
[Gamma[3/4]]</syntaxhighlight>
||
||{{OEIS2C|A062089}}
||[2;1,1,2,2,3,1,3,1,9,2,8,4,1,13,3,1,15,18,1,...]
||1907
||<small> 2.58498175957925321706589358738317116 </small>
|-

<!------------------------------------------v------------------------------------------->
|1.73245471460063347358 
||ثابت أويلر – ماتشيروني
||
|bgcolor=#e0f0f0 align=center|<math>\frac {1}{\gamma}</math>
||<math> \left(\int_{0}^{1} -\log \left(\log \frac{1}{x}\right)\, dx\right)^{-1} = \sum_{n=1}^\infty (-1)^n (-1+\gamma)^n </math>
||<syntaxhighlight lang="mathematica">1/Integrate_ 
 {x=0 to 1} 
 -log(log(1/x))</syntaxhighlight>
||
||{{OEIS2C|A098907}}
||[1;1,2,1,2,1,4,3,13,5,1,1,8,1,2,4,1,1,40,1,11,...]
||
||<small> 1.73245471460063347358302531586082968 </small> 
|-

<!--------------------------------------------v----------------------------------------->
| 1.435991124176917432355 
||ثابت يبيسج <ref>{{استشهاد بكتاب 
|مؤلف= Chebfun Team
|عنوان= Lebesgue functions and Lebesgue constants
|مسار= https://www.mathworks.com/matlabcentral/fileexchange/23972-chebfun-v4-old-version-please-download-current-version-instead
|سنة= 2010
|ناشر= MATLAB Central
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20160303203902/http://www.mathworks.com/matlabcentral/fileexchange/23972-chebfun/content/chebfun/examples/approx/html/LebesgueConst.html | تاريخ أرشيف = 3 مارس 2016 }}</ref><ref>{{استشهاد بكتاب
|مؤلف= Simon J. Smith
|عنوان= Lebesgue constants in polynomial interpolation
|مسار= http://www.emis.de/journals/AMI/2006/smith
|سنة= 2005
|ناشر= La Trobe University, Bendigo, Australia
|isbn=
| مسار أرشيف = https://web.archive.org/web/20200305205031/https://www.emis.de//journals/AMI/2006/smith | تاريخ أرشيف = 5 مارس 2020 }}</ref>
||[[ملف:Fourier series integral identities.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math>{L_1}</math>
||<math> \prod_{\begin{smallmatrix}i=0\\ j\neq i\end{smallmatrix}}^{n} \frac{x-x_i}{x_j-x_i} 
= \frac {1}{\pi} \int_0^{\pi} \frac {\lfloor \sin{\frac{3 t}{2}}\rfloor}{\sin{\frac{t}{2}}}\, dt = \frac {1}{3} + \frac {2 \sqrt{3}}{\pi} </math>
||<syntaxhighlight lang="mathematica">1/3 + 2*sqrt(3)/pi</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A226654}}
||[1;2,3,2,2,6,1,1,1,1,4,1,7,1,1,1,2,1,3,1,2,1,1,...]
||1902 ~
||<small> 1.43599112417691743235598632995927221 </small>
|-

<!----------------------------------------------v--------------------------------------->
|3.24697960371746706105 
||الجذر الفضي <ref>{{استشهاد بكتاب 
|مؤلف= D. R. Woodall
|عنوان= CHROMATIC POLYNOMIALS OF PLANE TRIANGULATIONS
|صفحة= 5
|سنة= 2005
|ناشر= University of Nottingham
|مسار= https://www.maths.nottingham.ac.uk/plp/pmadw/PG/cp.hndt.pdf
| مسار أرشيف = https://web.archive.org/web/20160303225540/https://www.maths.nottingham.ac.uk/personal/drw/PG/cp.hndt.pdf | تاريخ أرشيف = 3 مارس 2016 }}</ref>
||
|bgcolor=#e0f0f0 align=center|<math> \varsigma </math>
||<math> 2+2 \cos  \frac {2\pi} 7 = \textstyle 2+\frac{2+\sqrt[3]{7 + 7 \sqrt[3]{7 + 7 \sqrt[3]{\, 7 + \cdots}}}}{1+\sqrt[3]{7 + 7 \sqrt[3]{7 + 7 \sqrt[3]{\, 7 + \cdots}}}}</math>
||<syntaxhighlight lang="mathematica">2+2 cos(2Pi/7)</syntaxhighlight>
<!---2+(2+(7+7(7+7(7+7(7+7(7)^1/3)^1/3)^1/3)^1/3)^1/3)/(1+(7+7(7+7(7+7(7+7(7)^1/3)^1/3)^1/3)^1/3)^1/3)--->
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A116425}}
||[3;4,20,2,3,1,6,10,5,2,2,1,2,2,1,18,1,1,3,2,...]
||
||<small> 3.24697960371746706105000976800847962 </small>
|-

<!--------------------------------------------v----------------------------------------->
|1.94359643682075920505 
||[[مؤشر أويلر]] <ref>{{استشهاد بكتاب 
|مؤلف= Benjamin Klopsch
|عنوان= NOTE DI MATEMATICA: Representation growth and representation zeta functions of groups
|مسار= http://poincare.unile.it/adv2013/NOTE_VOL_33.pdf
|سنة= 2013
|ناشر= Università del Salento
|issn= 1590-0932 
|صفحة= 114
| مسار أرشيف = https://web.archive.org/web/20170220015746/http://poincare.unile.it/adv2013/NOTE_VOL_33.pdf | تاريخ أرشيف = 20 فبراير 2017 }}</ref><ref>{{استشهاد بكتاب 
|مؤلف= Nikos Bagis
|عنوان= Some New Results on Prime Sums (3 The Euler Totient constant)
|مسار= https://carma.newcastle.edu.au:443/resources/jon/Preprints/Papers/Submitted%20Papers/Elliptic%20moments/Papers/bagis.pdf
|سنة=  
|ناشر= Aristotle University of Thessaloniki
|isbn= 
|صفحة= 8
| مسار أرشيف = https://web.archive.org/web/20170220171643/https://carma.newcastle.edu.au/jon/Preprints/Papers/Submitted%20Papers/Elliptic%20moments/Papers/bagis.pdf | تاريخ أرشيف = 20 فبراير 2017 }}</ref>
||[[ملف:EulerPhi100.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>ET </math>
||<math>  \underset {p \text{= primes}}
{\prod_{p} \Big(1 + \frac{1}{p(p-1)}\Big)} = \frac {\zeta(2)\zeta(3)}{\zeta(6)}=\frac {315 \zeta(3)}{2\pi^4} </math>
||<syntaxhighlight lang="mathematica">zeta(2)*zeta(3)
/zeta(6)</syntaxhighlight>
||
||{{OEIS2C|A082695}}
||[1;1,16,1,2,1,2,3,1,1,3,2,1,8,1,1,1,1,1,1,1,32,...]
||1750
||<small> 1.94359643682075920505707036257476343 </small>
|-

<!--------------------------------------------v----------------------------------------->
|1.495348781221220541911
||[[جذر نوني|الجذر]] الرابع ل5 <ref>{{استشهاد بكتاب 
|مؤلف= Robinson, H.P.
|عنوان= MATHEMATICAL CONSTANTS.
|مسار= https://escholarship.org/uc/item/2t95c0bp
|سنة= 1971–2011
|ناشر= Lawrence Berkeley National Laboratory
|isbn= 
|صفحة= 40
| مسار أرشيف = https://web.archive.org/web/20190127034934/https://escholarship.org/uc/item/2t95c0bp | تاريخ أرشيف = 27 يناير 2019 }}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\sqrt[4]{5} </math>
||<math> \sqrt[5]{5 \,\sqrt[5]{5 \, \sqrt[5]{5 \,\sqrt[5]{5 \,\sqrt[5]{5  \,\cdots}}}}} </math>
||<syntaxhighlight lang="mathematica">(5(5(5(5(5(5(5) 
 ^1/5)^1/5)^1/5) 
 ^1/5)^1/5)^1/5) 
 ^1/5 ...</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A011003}}
||[1;2,53,4,96,2,1,6,2,2,2,6,1,4,1,49,17,2,3,2,...]
||
||<small> 1.49534878122122054191189899414091339 </small>
|-

<!------------------------------------------v------------------------------------------->
|0.87228404106562797617
||مساحة دائرة فورد <ref>{{استشهاد بكتاب
|مؤلف= Annmarie McGonagle
|عنوان= A New Parameterization for Ford Circles
|سنة= 2011
|ناشر= Plattsburgh State University of New York
|مسار= https://www.plattsburgh.edu/files/686/files/Mcgonaglevol%205p34-44.pdf
| مسار أرشيف = https://web.archive.org/web/20190127094142/https://www.plattsburgh.edu/files/686/files/Mcgonaglevol%205p34-44.pdf | تاريخ أرشيف = 27 يناير 2019 }}</ref> 
||[[ملف:Circumferències de Ford.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math> A_{CF} </math>
||<math> 
\sum_{q\ge 1} \sum_{ (p, q)=1 \atop 1 \le p < q }\pi \left( \frac{1}{2 q^2} \right)^2 
\underset {\zeta() \text{= Riemann Zeta Function}}
{= \frac{\pi}{4} \frac{\zeta(3)}{\zeta(4)}
= \frac{45}{2} \frac{\zeta(3)}{\pi^3}}
</math>
||<syntaxhighlight lang="mathematica">pi Zeta(3) 
/(4 Zeta(4))</syntaxhighlight>
||
||
||[0;1,6,1,4,1,7,5,36,3,29,1,1,10,3,2,8,1,1,1,3,...]
||
||<small> 0.87228404106562797617519753217122587 </small>
|-

<!---------------------------------------------v---------------------------------------->
| 1.08232323371113819151 
||[[دالة زيتا لريمان|زيتا]](4) <ref>{{استشهاد بكتاب 
|مؤلف= V. S. Varadarajan
|عنوان= Euler Through Time: A New Look at Old Themes
|مسار= https://books.google.com/?id=CYyKTREGYd0C&pg=PA60&dq=1.08232323371113819#v=onepage&q=1.08232323371113819&f=false
|سنة= 2000 
|ناشر= AMS
|isbn= 0-8218-3580-7
|مسار أرشيف= https://web.archive.org/web/20200615194453/https://books.google.com/books?id=CYyKTREGYd0C&pg=PA60&dq=1.08232323371113819&hl=fr#v=onepage&q=1.08232323371113819&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>\zeta(4)</math>
||<math> \frac{\pi^4}{90} = \sum_{n=1}^\infty\frac{{1}}{n^4} = \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \frac{1}{4^4} + \frac{1}{5^4} + ... </math>
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞]
{1/n^4}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A013662}}
||[1;12,6,1,3,1,4,183,1,1,2,1,3,1,1,5,4,2,7,23,...]
||?
||<small> 1.08232323371113819151600369654116790 </small>
|-

<!---------------------------------------------v---------------------------------------->
|1.56155281280883027491
||[[عدد مثلثي تربيعي|عدد مثلثي مربعي]] للرقم 2.<ref>{{استشهاد بكتاب 
|مؤلف1=Leonhard Euler |مؤلف2=Joseph Louis Lagrange |عنوان= Elements of Algebra, Volumen 1
|مسار= https://books.google.com/?id=hqI-AAAAYAAJ&pg=PA334&dq=%22triangular+root%22#v=onepage&q=%22triangular%20root%22&f=false
|سنة= 1810
|ناشر= J. Johnson and Company
|isbn= 
|صفحة= 333
|مسار أرشيف= https://web.archive.org/web/20200304173010/https://books.google.com/?id=hqI-AAAAYAAJ&pg=PA334&dq=%22triangular+root%22#v=onepage&q=%22triangular%20root%22&f=false|تاريخ أرشيف=2020-03-04}}</ref> 
||[[ملف:Números triangulares.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>{R_2}</math>
||<math>\frac{\sqrt{17}-1}{2} = \,\scriptstyle \sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\sqrt{4+\cdots}}}}}} \,\, -1 </math>
<math> = \,\scriptstyle \sqrt{4-\sqrt{4-\sqrt{4-\sqrt{4-\sqrt{4-\sqrt{4-\cdots}}}}}} \textstyle </math>
||<syntaxhighlight lang="mathematica">(sqrt(17)-1)/2</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A222133}}
||[1;1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,1,3,1,...] <br /> [1;{{سطر فوقي|1,1,3}}]
||
||<small> 1.56155281280883027491070492798703851 </small>
|-

<!-------------------------------------------v------------------------------------------>
|9.86960440108935861883
||[[مربع (جبر)|مربع]] [[باي (توضيح)|باي]]
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>{\pi} ^2</math>
||<math>6\, \zeta(2) = 6 \sum_{n=1}^\infty \frac{1}{n^2} = \frac{6}{1^2} + \frac{6}{2^2} + \frac{6}{3^2} + \frac{6}{4^2}+ \cdots</math>
||<syntaxhighlight lang="mathematica">6 Sum[n=1 to ∞]
{1/n^2}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||[http://oeis.org/A002388 A002388]
||[9;1,6,1,2,47,1,8,1,1,2,2,1,1,8,3,1,10,5,1,3,...]
||
||<small> 9.86960440108935861883449099987615114 </small>
|-

<!---------------------------------------------v---------------------------------------->
|1.32471795724474602596
||[[عدد بلاستيكي|العدد البلاستيكي]] <ref>{{استشهاد بكتاب 
|مؤلف= Ian Stewart
|عنوان= Professor Stewart's Cabinet of Mathematical Curiosities
|مسار= https://books.google.com/?id=oW6Xeo8EmDgC&pg=PT120&dq=%22Plastic+number%22#v=onepage&q=%22Plastic%20number%22&f=false
|سنة= 1996
|ناشر= Birkhäuser Verlag
|isbn= 978-1-84765-128-0
|مسار أرشيف= https://web.archive.org/web/20200304173012/https://books.google.com/?id=oW6Xeo8EmDgC&pg=PT120&dq=%22Plastic+number%22#v=onepage&q=%22Plastic%20number%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Nombre plastique.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{\rho}</math>
||<math>\sqrt[3]{1 + \! \sqrt[3]{1 + \! \sqrt[3]{1 + \cdots}}} = \textstyle \sqrt[3]{\frac{1}{2}+ \! \sqrt{\frac{23}{108}}}+ \! \sqrt[3]{\frac{1}{2}- \! \sqrt{\frac{23}{108}}}</math>
||<syntaxhighlight lang="mathematica">(1+(1+(1+(1+(1+(1)
^(1/3))^(1/3))^(1/3))
^(1/3))^(1/3))^(1/3)</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A060006}}
||[1;3,12,1,1,3,2,3,2,4,2,141,80,2,5,1,2,8,2,...]
||1929
||<small> 1.32471795724474602596090885447809734 </small>
|-

<!------------------------------------------v------------------------------------------->
|2.37313822083125090564
||ثابت ليفي<sub>2</sub> <ref name="books.google.com">{{استشهاد بكتاب 
|مؤلف= H.M. Antia
|عنوان= Numerical Methods for Scientists and Engineers
|مسار= https://books.google.com/?id=YzXsZgjyFA4C&pg=PA220&dq=1.772453850905516#v=onepage&q=1.772453850905516&f=false
|سنة= 2000
|ناشر= Birkhäuser Verlag
|isbn= 3-7643-6715-6
|صفحة= 220
|مسار أرشيف= https://web.archive.org/web/20200304173014/https://books.google.com/?id=YzXsZgjyFA4C&pg=PA220&dq=1.772453850905516#v=onepage&q=1.772453850905516&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>2\,ln\,\gamma </math>
||<math>\frac{\pi^2}{6ln(2)} </math>
||<syntaxhighlight lang="mathematica">Pi^(2)/(6*ln(2))</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A174606}}
||[2;2,1,2,8,57,9,32,1,1,2,1,2,1,2,1,2,1,3,2,...]
||1936
||<small> 2.37313822083125090564344595189447424 </small>
|-

<!------------------------------------------v------------------------------------------->
|0.85073618820186726036
||متسلسلة طوي الورق <ref>{{استشهاد بكتاب  
|مؤلف1=Francisco J. Aragón Artacho |مؤلف2=David H. Baileyy |مؤلف3=Jonathan M. Borweinz |مؤلف4=Peter B. Borwein |عنوان= Tools for visualizing real numbers.
|مسار= https://carma.newcastle.edu.au:443/resources/jon/tools1.pdf
|سنة= 2012
|ناشر= 
|isbn= 
|صفحة= 33
| مسار أرشيف = https://web.archive.org/web/20170220175429/https://carma.newcastle.edu.au/jon/tools1.pdf | تاريخ أرشيف = 20 فبراير 2017 }}</ref><ref>{{استشهاد بكتاب
|عنوان= Papierfalten
|مسار= http://www.jgiesen.de/Divers/PapierFalten/PapierFalten.pdf
|سنة= 1998
|ناشر= 
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20170220015655/http://www.jgiesen.de/Divers/PapierFalten/PapierFalten.pdf | تاريخ أرشيف = 20 فبراير 2017 }}</ref>
||[[ملف:Miura-ori.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math>{P_f}</math>
||<math> \sum_{n=0}^{\infty} \frac {8^{2^n}}{2^{2^{n+2}}-1} = 
\sum_{n=0}^{\infty} \cfrac {\tfrac {1}{2^{2^n}}} {1-\tfrac{1}{2^{2^{n+2}}}} </math>
|| <syntaxhighlight lang="mathematica">N[Sum[n=0 to ∞]
 {8^2^n/(2^2^ 
 (n+2)-1)},37]</syntaxhighlight>
||
||{{OEIS2C|A143347}}
||[0;1,5,1,2,3,21,1,4,107,7,5,2,1,2,1,1,2,1,6,...]
||
||<small> 0.85073618820186726036779776053206660 </small>
|-

<!------------------------------------------v------------------------------------------->
| 1.1563626843322697168533
||ثابت تكرار المكعب <ref>{{استشهاد بدورية محكمة 
|عنوان= The generalized-Euler-constant function γ(z) and a generalization of Somos's quadratic recurrence constant
|سنة= 2008 
|الأول1= Jonathan |الأخير1=Sondow 
|الأول2= Petros|الأخير2= Hadjicostas 
|doi= 10.1016/j.jmaa.2006.09.081 
|صحيفة= Journal of Mathematical Analysis and Applications 
|المجلد= 332 
|صفحات= 292–314
|arxiv=math/0610499
}}</ref><ref>
{{استشهاد بدورية محكمة
|مؤلف= J. Sondow
|سنة=2007
|عنوان= Generalization of Somos Quadratic
|صحيفة= Journal of Mathematical Analysis and Applications
|المجلد= 332
|العدد=
|صفحات= 292–314
|arxiv=math/0610499
|doi= 10.1016/j.jmaa.2006.09.081
}}</ref>
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>{\sigma_3}</math>
||<math>\prod_{n=1}^\infty n^{{3}^{-n}} = \sqrt[3] {1 \sqrt[3] {2 \sqrt[3]{3 \cdots}}} = 1^{1/3} \; 2^{1/9} \; 3^{1/27} \cdots </math>
||<syntaxhighlight lang="mathematica">prod[n=1 to ∞]
{n ^(1/3)^n}</syntaxhighlight>
||
||{{OEIS2C|A123852}}
||[1;6,2,1,1,8,13,1,3,2,2,6,2,1,2,1,1,1,10,33,...]
||
||<small> 1.15636268433226971685337032288736935 </small>
|-

<!-------------------------------------------v------------------------------------------>
| 1.261859507142914874199 
||البعد الكسري لمنحنى [[ندفة الثلج لكوخ]] <ref>{{استشهاد بكتاب 
|مؤلف= Chan Wei Ting ...
|عنوان= Moire patterns + fractals
|صفحة=16
|مسار= https://www.math.nus.edu.sg/aslaksen/gem-projects/maa/0304-2-02-Moire_Patterns_and_Fractals.pdf
| مسار أرشيف = https://web.archive.org/web/20181123123942/http://www.math.nus.edu.sg/aslaksen/gem-projects/maa/0304-2-02-Moire_Patterns_and_Fractals.pdf | تاريخ أرشيف = 23 نوفمبر 2018 }}</ref> 
||[[ملف:Koch snowflake05.ogv|100px]]
|bgcolor=#e0f0f0 align=center|<math>{C_k}</math>
||<math> \frac{\log 4}{\log 3} </math>
||<syntaxhighlight lang="mathematica">log(4)/log(3)</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||[http://oeis.org/A100831 A100831]
||[1;3,1,4,1,1,11,1,46,1,5,112,1,1,1,1,1,3,1,7,...]
||
||<small> 1.26185950714291487419905422868552171 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|6.58088599101792097085
||ثابت فورودا<ref>{{استشهاد بكتاب 
|مؤلف= Christoph Zurnieden
|عنوان= Descriptions of the Algorithms
|مسار= http://pragmath.sourceforge.net/algorithms.pdf
|سنة= 2008 
|ناشر= 
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20160303191626/http://pragmath.sourceforge.net/algorithms.pdf | تاريخ أرشيف = 3 مارس 2016 }}</ref>
||<br /><br />
|bgcolor=#e0f0f0 align=center|<math>2^{\,e} </math>
||<math>2^e  </math>
||<syntaxhighlight lang="mathematica">2^e</syntaxhighlight>
||
||
||[6;1,1,2,1,1,2,3,1,14,11,4,3,1,1,7,5,5,2,7,...]
||
||<small> 6.58088599101792097085154240388648649 </small>
|-

<!-----------------------------------------v-------------------------------------------->
|0.26149 72128 47642 78375 
||ثابت [[فرانز ميرتنز|ميرتنز]]-ميسيل <ref>{{استشهاد بكتاب 
|مؤلف= Julian Havil
|عنوان= Gamma: Exploring Euler's Constant
|مسار= https://books.google.com/?id=7-sDtIy8MNIC&pg=PA161&dq=Khinchin%27s+constant#v=onepage&q=Khinchin%27s%20constant&f=false
|سنة= 2003 
|ناشر= Princeton University Press
|isbn= 9780691141336 
|صفحة= 64
|مسار أرشيف= https://web.archive.org/web/20200304173016/https://books.google.com/?id=7-sDtIy8MNIC&pg=PA161&dq=Khinchin%27s+constant#v=onepage&q=Khinchin%27s%20constant&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Meissel–Mertens constant definition.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{M}</math>
||<math>\lim_{n \rightarrow \infty } \!\! \left( 
\sum_{p \leq n} \frac{1}{p} \! - \ln(\ln(n))\! \right) \!\! =
\underset{\!\!\!\! \gamma: \, \text{Euler constant} ,\,\, 
p: \, \text{prime}}{\! \gamma \! + \!\! \sum_{p} \!\left( \! 
\ln \! \left( \! 1 \! - \! \frac{1}{p} \! \right)
 \!\! + \! \frac{1}{p} \! \right)}</math>
||<syntaxhighlight lang="mathematica">gamma+ 
 Sum[n=1 to ∞] 
 {ln(1-1/prime(n)) 
 +1/prime(n)}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A077761}}
||[0;3,1,4,1,2,5,2,1,1,1,1,13,4,2,4,2,1,33,296,...]
||1866 <br /> & <br /> 1873
||<small> 0.26149721284764278375542683860869585 </small>
|-

<!------------------------------------------v------------------------------------------->
|4.81047738096535165547
||ثابت جون <ref>{{استشهاد بكتاب 
|مؤلف= Steven R. Finch 
|عنوان= Mathematical Constants
|مسار= https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA466&lpg=PA466&dq=4.810477#v=onepage&q=4.810477&f=false
|سنة= 2003 
|ناشر= Cambridge University Press
|isbn= 3-540-67695-3
|صفحة= 466
|مسار أرشيف= https://web.archive.org/web/20200304173021/https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA466&lpg=PA466&dq=4.810477#v=onepage&q=4.810477&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
| bgcolor=#e0f0f0 align=center|<math> \gamma </math>
||<math>\sqrt[i]{i} = i^{-i} = (i^i)^{-1} = (((i)^i)^i)^i = e^{\frac{\pi}{2}} = \sqrt{\sum_{n=0}^\infty \frac{\pi^{n}}{n!}}</math>
||<syntaxhighlight lang="mathematica">e^(π/2)</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A042972}}
||[4;1,4,3,1,1,1,1,1,1,1,1,7,1,20,1,3,6,10,3,2,...]
||
||<small> 4.81047738096535165547303566670383313 </small>
|-

<!-----------------------------------------v-------------------------------------------->
| - 0.5 <br/> ± 0.86602540378443 '''''i'''''
||[[جذر تكعيبي|الجذر التكعيبي]] للرقم 1 <ref>{{استشهاد بكتاب
|مؤلف= James Stuart Tanton
|عنوان= Encyclopedia of Mathematics
|صفحة= 458
|سنة= 2007
|ناشر= 
|isbn= 0-8160-5124-0
|مسار= https://books.google.com/?id=MfKKMSuthacC&pg=PA358&dq=%22Root+of+unity%22#v=onepage&q=%22Root%20of%20unity%22&f=false
|مسار أرشيف= https://web.archive.org/web/20200304173024/https://books.google.com/?id=MfKKMSuthacC&pg=PA358&dq=%22Root+of+unity%22#v=onepage&q=%22Root%20of%20unity%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:3rd roots of unity.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>\sqrt[3]{1}</math>
||<math> \begin{cases} \ \ 1 \\ -\frac{1}{2}+\frac{\sqrt{3}}{2}i \\ -\frac{1}{2}-\frac{\sqrt{3}}{2}i. \end{cases} </math>
||<syntaxhighlight lang="mathematica">1, 
 E^(2i pi/3), 
 E^(-2i pi/3)</syntaxhighlight>
|'''[[عدد مركب|خ]]'''<br /> '''[[عدد جبري|ج]]'''
||{{OEIS2C|A010527}}
||- [0,5] <br /> ± [0;1,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,6,2,...] i <br /> - [0,5] <br /> ± [0; 1, {{سطر فوقي|6, 2}}] i
||
||<small> - 0.5 <br/> ± 0.8660254037844386467637231707529 '''''i''''' </small> 
|-

<!---------------------------------------------v---------------------------------------->
|0.110001000000000000000001
||عدد [[جوزيف ليوفيل|ليوفيل]] <small>نص صغير</small><ref>{{استشهاد بكتاب 
|مؤلف= Calvin C. Clawson
|عنوان= Mathematical Traveler: Exploring the Grand History of Numbers
|مسار= https://books.google.com/?id=E3Eu3sV_anUC&pg=PA187&dq=Liouville+number+0.11000100000000000000000100#v=onepage&q=Liouville%20number%200.11000100000000000000000100&f=false
|سنة= 2003 
|ناشر= Perseus
|isbn= 0-7382-0835-3
|صفحة= 187 
| مسار أرشيف = https://web.archive.org/web/20200305205044/https://books.google.com/?id=E3Eu3sV_anUC&pg=PA187&dq=Liouville+number+0.11000100000000000000000100#v=onepage&q=Liouville%20number%200.11000100000000000000000100&f=false | تاريخ أرشيف = 5 مارس 2020 }}</ref>
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>\text{£}_{Li}</math>
||<math> \sum_{n=1}^\infty \frac{1}{10^{n!}} = \frac {1}{10^{1!}} + \frac{1}{10^{2!}} + \frac{1}{10^{3!}} + \frac{1}{10^{4!}}  + \cdots</math>
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞] 
 {10^(-n!)}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A012245}}
||[1;9,1,999,10,9999999999999,1,9,999,1,9]
||
||<small> 0.11000100000000000000000100... </small>
|-

<!-----------------------------------------v-------------------------------------------->
|0.06598803584531253707
||النهاية الصغرى ل[[رفع (رياضيات)|رفع]] [[دالة أسية|الأساس e]] بالأس e.<ref>{{استشهاد بكتاب 
|مؤلف1=Jonathan Sondowa |مؤلف2=Diego Marques |عنوان= Algebraic and transcendental solutions of some exponential equations
|مسار= http://ami.ektf.hu/uploads/papers/finalpdf/AMI_37_from151to164.pdf
|سنة= 2010
|ناشر= Annales Mathematicae et Informaticae
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20190828213120/http://ami.ektf.hu/uploads/papers/finalpdf/AMI_37_from151to164.pdf | تاريخ أرشيف = 28 أغسطس 2019 }}</ref>
||[[ملف:Infinite power tower.svg|80px]]
|bgcolor=#e0f0f0 align=center|<math>{e}^{-e}</math>
||<math>\left(\frac {1}{e}\right)^e</math>
||<syntaxhighlight lang="mathematica">1/(e^e)</syntaxhighlight>
||
||{{OEIS2C|A073230}}
||[0;15,6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,...]
||
||<small> 0.06598803584531253707679018759684642 </small> 
|-

<!----------------------------------------v--------------------------------------------->
|1.83928675521416113255
||ثابت تريبوناكسي<ref>{{استشهاد بكتاب
|مؤلف= T. Piezas.
|عنوان= Tribonacci constant & Pi
|مسار= https://sites.google.com/site/tpiezas/0012
| مسار أرشيف = https://web.archive.org/web/20180414023400/https://sites.google.com/site/tpiezas/0012 | تاريخ أرشيف = 14 أبريل 2018 }}</ref>
||
|bgcolor=#e0f0f0 align=center|<math> {\phi_{}}_3 </math>
||<math>\textstyle \frac{1+\sqrt[3]{19+3\sqrt{33}}+\sqrt[3]{19-3\sqrt{33}}}{3} = \scriptstyle \, 1+ \left(\sqrt[3]{\tfrac12 + \sqrt[3]{\tfrac12 + \sqrt[3]{\tfrac12 + ...}}}\right)^{-1}</math>
||<syntaxhighlight lang="mathematica">(1/3)*(1+(19+3 
 *sqrt(33))^(1/3) 
 +(19-3 
 *sqrt(33))^(1/3))</syntaxhighlight>
<!--- 1+1/(((((((1/2)^(1/3)+1/2)^(1/3)+1/2)^(1/3)+1/2)^(1/3)+1/2)^(1/3)+1/2)^(1/3)) --->
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A058265}}
||[1;1,5,4,2,305,1,8,2,1,4,6,14,3,1,13,5,1,7,...]
||
||<small> 1.83928675521416113255185256465328660 </small>
|-

<!--------------------------------------------v----------------------------------------->
| 0.366512920581664327012
||متوسط توزيع جامبل <ref>{{استشهاد بكتاب
|مؤلف= Steven Finch
|عنوان= Addenda to Mathematical Constants
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf
| مسار أرشيف = https://web.archive.org/web/20160316175639/http://www.people.fas.harvard.edu/~sfinch/csolve/erradd.pdf | تاريخ أرشيف = 16 مارس 2016 }}</ref>
||[[ملف:GumbelDichteF.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{ll_2}</math>
||<math>-\ln(\ln(2)) </math>
||<syntaxhighlight lang="mathematica">-ln(ln(2))</syntaxhighlight>
||
||[http://oeis.org/A074785 A074785]
||[0;2,1,2,1,2,6,1,6,6,2,2,2,1,12,1,8,1,1,3,1,...]
||
||<small> 0.36651292058166432701243915823266947 </small>
|-

<!----------------------------------------------v--------------------------------------->
| 36.46215960720791177099
||[[باي (توضيح)|باي]] مرفوع ب[[رفع (رياضيات)|الأس]] [[باي (توضيح)|باي]] <ref>{{استشهاد بكتاب 
|مؤلف= Renzo Sprugnoli.
|عنوان= Introduzione alla Matematica
|مسار= http://www.dsi.unifi.it/~resp/media.pdf 
|سنة=  
|ناشر= 
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20170422044502/http://www.dsi.unifi.it/~resp/media.pdf | تاريخ أرشيف = 22 أبريل 2017 }}</ref>
||<br /><br />
|bgcolor=#e0f0f0 align=center|<math>\pi ^\pi</math>
||<math>\pi ^\pi</math>
||<syntaxhighlight lang="mathematica">pi^pi</syntaxhighlight>
||
||{{OEIS2C|A073233}}
||[36;2,6,9,2,1,2,5,1,1,6,2,1,291,1,38,50,1,2,...]
||
||<small> 36.4621596072079117709908260226921236 </small>
|-

<!---------------------------------------------v---------------------------------------->
|0.53964549119041318711
||ثابت إيواتشيميسكو<ref>{{استشهاد بكتاب 
|مؤلف= Chao-Ping Chen
|عنوان= Ioachimescu's constant
|مسار= https://ajmaa.org/RGMIA/papers/v13n1/chen.pdf
|سنة=  
|ناشر= 
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20131215032055/http://ajmaa.org/RGMIA/papers/v13n1/chen.pdf | تاريخ أرشيف = 15 ديسمبر 2013 }}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>2+\zeta(\tfrac12)</math>
||<math>{2{-}(1{+}\sqrt{2})\sum_{n=1}^\infty \frac{(-1)^{n+1}}{\sqrt{n}}} = \gamma + \sum_{n=1}^\infty \frac{(-1)^{2n} \; \gamma_n}{2^n n!} </math>
||<syntaxhighlight lang="mathematica">γ + N[
sum[n=1 to ∞] 
 {((-1)^(2n) 
 gamma_n)
/(2^n n!)}]</syntaxhighlight>
||
||2-<br/>{{OEIS2C|A059750}}
||[0;1,1,5,1,4,6,1,1,2,6,1,1,2,1,1,1,37,3,2,1,...]
||
||<small> 0.53964549119041318711050084748470198 </small>
|-

<!-----------------------------------------v-------------------------------------------->
|15.1542622414792641897
||مجموعة الهروب <ref>{{استشهاد بكتاب 
|مؤلف= R. A. Knoebel.
|عنوان= Exponentials Reiterated
|مسار= https://www.maa.org/sites/default/files/pdf/upload_library/22/Chauvenet/Knoebelchv.pdf
|سنة=  
|ناشر= Maa.org
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20170329032456/http://www.maa.org/sites/default/files/pdf/upload_library/22/Chauvenet/Knoebelchv.pdf | تاريخ أرشيف = 29 مارس 2017 }}</ref>
||[[ملف:Exp-esc.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>e^e</math>
||<math> \sum_{n=0}^\infty \frac{e^n}{n!} = \lim_{n \to \infty} \left(\frac {1+n}{n} \right)^{n^{-n}(1+n)^{1+n}} </math>
||<syntaxhighlight lang="mathematica">Sum[n=0 to ∞]
{(e^n)/n!}</syntaxhighlight>
||
||{{OEIS2C|A073226}}
||[15;6,2,13,1,3,6,2,1,1,5,1,1,1,9,4,1,1,1,6,7,...]
||
||<small> 15.1542622414792641897604302726299119 </small>
|-

<!-------------------------------------------v------------------------------------------>
|0.64624543989481330426
||ثابت جرمين-ماصر <ref>{{استشهاد بكتاب 
|مؤلف= Eric W. Weisstein 
|عنوان= CRC Concise Encyclopedia of Mathematics, Second Edition
|مسار= https://books.google.com/?id=aFDWuZZslUUC&pg=PA1861&lpg=PA1861&dq=masser+gramain+constant#v=onepage&q=masser%20gramain%20constant&f=false
|سنة= 2003 
|ناشر= CRC Press
|isbn= 1-58488-347-2
|صفحة= 1688
|مسار أرشيف= https://web.archive.org/web/20200304173027/https://books.google.com/books?id=aFDWuZZslUUC&pg=PA1861&lpg=PA1861&dq=masser+gramain+constant&hl=en#v=onepage&q=masser%20gramain%20constant&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{C}</math>
||<math> \gamma {\beta}(1) \! + \! {\beta}'(1) \! = \pi \! \left(-\!\ln \Gamma(\tfrac14)+\tfrac34 \pi+\tfrac12 \ln 2+\tfrac12 \gamma \right) </math>
<math> = \pi \! \left(-\!\ln (\tfrac14 !)+\tfrac34 \ln \pi -\tfrac32 \ln 2+\tfrac12 \, \gamma \right) </math> <math>\scriptstyle \gamma = \text{Euler–Mascheroni constant}= 0.5772156649\ldots</math>
<math>\scriptstyle \beta() = \text{Beta function} , \quad \scriptstyle \Gamma() = \text{Gamma function}</math>
||<syntaxhighlight lang="mathematica">Pi/4*(2*Gamma 
+ 2*Log[2]
 + 3*Log[Pi]- 4 
 Log[Gamma[1/4]])</syntaxhighlight> 
||
||{{OEIS2C|A086057}}
||[0;1,1,1,4,1,3,2,3,9,1,33,1,4,3,3,5,3,1,3,4,...]
||
||<small> 0.64624543989481330426647339684579279 </small>
|-

<!------------------------------------------v------------------------------------------->
|1.11072073453959156175
||النسبة بين [[مربع]] محاط ب[[دائرة]] <ref>{{استشهاد بأرخايف 
|author= Richard J.Mathar.
|title= Table of Dirichlet L-series and Prime Zeta
|arxiv= 1008.2547
|year=2010
|class=math.NT
}}</ref>
||[[ملف:Circumscribed2.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>\frac{\pi}{2\sqrt 2}</math>
||<math>\sum_{n = 1}^\infty \frac{({-}1)^{\lfloor \frac{n-1}{2}\rfloor}}{2n+1} = \frac{1}{1} + \frac{1}{3} - \frac{1}{5} - \frac{1}{7} + \frac{1}{9} + \frac{1}{11} - {\cdots}</math>
||<syntaxhighlight lang="mathematica">sum[n=1 to ∞]
{(-1)^(floor(
(n-1)/2))
/(2n-1)}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A093954}}
||[1;9,31,1,1,17,2,3,3,2,3,1,1,2,2,1,4,9,1,3,...]
||
||<small> 1.11072073453959156175397024751517342 </small> 
|-

<!----------------------------------------------v--------------------------------------->
|1.45607494858268967139
||ثابت باكهاوس <ref>{{استشهاد بكتاب 
|مؤلف= Eric W. Weisstein
|عنوان= CRC Concise Encyclopedia of Mathematics, Second Edition
|مسار= https://books.google.com/?id=aFDWuZZslUUC&pg=PA151&dq=Backhouse+constant#v=onepage&q=%22Backhouse%20constant%22&f=false
|سنة= 2003 
|ناشر= CRC Press
|isbn= 1-58488-347-2
|صفحة= 151
|مسار أرشيف= https://web.archive.org/web/20200614120804/https://books.google.com/books?id=aFDWuZZslUUC&pg=PA151&dq=Backhouse+constant&hl=fr#v=onepage&q=%22Backhouse%20constant%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{B}</math>
||<math>\lim_{k \to \infty}\left | \frac{q_{k+1}}{q_k} \right \vert  \quad \scriptstyle \text {where:} \displaystyle \;\; Q(x)=\frac{1}{P(x)}= \! \sum_{k=1}^\infty q_k x^k  </math>
<math> P(x) =  \sum_{k=1}^\infty \underset{p_k\text{ prime}}{p_k x^k} = 1+2x+3x^2+5x^3+\cdots</math>
||<syntaxhighlight lang="mathematica">1/( FindRoot[0 == 1 + 
Sum[x^n Prime[n], 
{n, 10000}], {x, {1}})</syntaxhighlight>
||
||{{OEIS2C|A072508}}
||[1;2,5,5,4,1,1,18,1,1,1,1,1,2,13,3,1,2,4,16,...]
||1995
||<small> 1.45607494858268967139959535111654355 </small>
|-

<!--------------------------------------------v----------------------------------------->
|1.85193705198246617036
||ثابت غيبس <ref>{{استشهاد بكتاب 
|مؤلف= Dave Benson
|عنوان= Music: A Mathematical Offering
|مسار= https://books.google.com/?id=Ko1NsIq4qLIC&pg=PA53&dq=1.8519370#v=onepage&q=1.8519370&f=false
|سنة= 2006 
|ناشر= Cambridge University Press
|isbn= 978-0-521-85387-3 
|صفحة= 53
|مسار أرشيف= https://web.archive.org/web/20200304173031/https://books.google.com/?id=Ko1NsIq4qLIC&pg=PA53&dq=1.8519370#v=onepage&q=1.8519370&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Sine integral.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{Si(\pi)}</math> <br/> [[تكامل مثلثي|تكامل الجيب]]
||<math> \int_0^{\pi} \frac {\sin t}{t}\, dt =
\sum \limits_{n=1}^\infty (-1)^{n-1} \frac{\pi^{2n-1}}{(2n-1)(2n-1)!} </math> <br/>
<math> =  \pi- \frac{\pi^3}{3\cdot3!} + \frac{\pi^5}{5\cdot5!} - \frac{\pi^7}{7\cdot7!} + \cdots  </math>
||<syntaxhighlight lang="mathematica">SinIntegral[Pi]</syntaxhighlight>
||
||{{OEIS2C|A036792}}
||[1;1,5,1,3,15,1,5,3,2,7,2,1,62,1,3,110,1,39,...]
||
||<small> 1.85193705198246617036105337015799136 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|0.23571113171923293137
||ثابت كوبلاند – إيردوس <ref>{{استشهاد بكتاب 
|مؤلف= Yann Bugeaud 
|عنوان= Distribution Modulo One and Diophantine Approximation
|مسار= https://books.google.com/?id=NeEpoAf7k0IC&pg=PA87&dq=0.235711131719232931#v=onepage&q=0.235711131719232931&f=false
|سنة=  2012
|ناشر= Cambridge University Press
|isbn=978-0-521-11169-0
|صفحة= 87
|مسار أرشيف= https://web.archive.org/web/20200304173033/https://books.google.com/?id=NeEpoAf7k0IC&pg=PA87&dq=0.235711131719232931#v=onepage&q=0.235711131719232931&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\mathcal{C}_{CE}}</math>
||<math>\sum _{n=1}^\infty \frac{p_n} {10^{n + \sum \limits_{k=1}^n \lfloor \log_{10}{p_k} \rfloor }}</math> 
||<syntaxhighlight lang="mathematica">sum[n=1 to ∞] 
 {prime(n) /(n+(10^ 
 sum[k=1 to n]{floor 
 (log_10 prime(k))}))}</syntaxhighlight>
|'''[[عدد غير كسري|غ.ك]]'''
||{{OEIS2C|A033308}}
||[0;4,4,8,16,18,5,1,1,1,1,7,1,1,6,2,9,58,1,3,...]
||
||<small> 0.23571113171923293137414347535961677 </small>
|-

<!-----------------------------------------v-------------------------------------------->
|1.523627086202492106277
||البعد الكسري لمنحني التنين <ref>{{استشهاد بكتاب 
|مؤلف= Angel Chang y Tianrong Zhang
|عنوان= On the Fractal Structure of the Boundary of Dragon Curve
|مسار= http://poignance.coiraweb.com/math/Fractals/Dragon/Bound.html
|سنة=  
|ناشر= 
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20190816094554/http://poignance.coiraweb.com/math/Fractals/Dragon/Bound.html | تاريخ أرشيف = 16 أغسطس 2019 }}</ref>
||[[ملف:Fractal dragon curve.jpg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{C_d}</math>
||<math>\frac{\log\left(\frac{1+\sqrt[3]{73-6\sqrt{87}}+\sqrt[3]{73+6\sqrt{87}}}{3}\right)}
{\log(2)}</math>
||<syntaxhighlight lang="mathematica">(log((1+(73-6 sqrt(87))^1/3+ 
(73+6 sqrt(87))^1/3)/3))/ 
log(2)))</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||
||[1;1,1,10,12,2,1,149,1,1,1,3,11,1,3,17,4,1,...]
||
||<small> 1.52362708620249210627768393595421662 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|1.78221397819136911177 
||ثابت جروثينديك<ref>{{استشهاد بكتاب 
|مؤلف= Joe Diestel
|عنوان= Absolutely Summing Operators
|مسار= https://books.google.com/?id=pHqyRSdgVTsC&pg=PA29&lpg=PA29&dq=1.782+GROTHENDIECK#v=onepage&q=1.782%20GROTHENDIECK&f=false
|سنة= 1995 
|ناشر= Cambridge University Press
|isbn= 0-521-43168-9
|صفحة= 29
|مسار أرشيف= https://web.archive.org/web/20200304173035/https://books.google.com/?id=pHqyRSdgVTsC&pg=PA29&lpg=PA29&dq=1.782+GROTHENDIECK#v=onepage&q=1.782%20GROTHENDIECK&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>{K_{R}}</math>
||<math> \frac {\pi}{2 \log(1+\sqrt{2})} </math>
||<syntaxhighlight lang="mathematica">pi/(2 log(1+sqrt(2)))</syntaxhighlight>
||
||{{OEIS2C|A088367}}
||[1;1,3,1,1,2,4,2,1,1,17,1,12,4,3,5,10,1,1,3,...]
||
||<small> 1.78221397819136911177441345297254934 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|1.58496250072115618145
||[[بعد هاوسدورف]]، [[مثلث سيربنسكي]] <ref>{{استشهاد بكتاب 
|مؤلف= Eric W. Weisstein
|عنوان= CRC Concise Encyclopedia of Mathematics, Second Edition
|مسار= https://books.google.com/?id=aFDWuZZslUUC&pg=PA2685&dq=1.584962500#v=onepage&q=1.584962500&f=false
|سنة= 2002  
|ناشر= CRC Press
|isbn= 1-58488-347-2
|صفحة= 1356
|مسار أرشيف= https://web.archive.org/web/20200304173003/https://books.google.com/?id=aFDWuZZslUUC&pg=PA2685&dq=1.584962500#v=onepage&q=1.584962500&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:SierpinskiTriangle-ani-0-7.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math>{log_2 3}</math>
||<math>\frac {\log 3}{\log 2} = \frac{\sum_{n=0}^\infty \frac{1}{2^{2n+1}(2n+1)}}{\sum_{n=0}^\infty \frac{1}{3^{2n+1}(2n+1)}} = \frac{\frac{1}{2}+\frac{1}{24}+\frac{1}{160}+\cdots}{\frac{1}{3}+\frac{1}{81}+\frac{1}{1215}+\cdots} </math>
||<syntaxhighlight lang="mathematica">( Sum[n=0 to ∞] {1/
(2^(2n+1) (2n+1))})/ 
 (Sum[n=0 to ∞] {1/
(3^(2n+1) (2n+1))})</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A020857}}
||[1;1,1,2,2,3,1,5,2,23,2,2,1,1,55,1,4,3,1,1,...]
||
||<small> 1.58496250072115618145373894394781651 </small> 
|-

<!-------------------------------------------v------------------------------------------>
| 1.30637788386308069
||[[ثابت ميلز]] <ref>{{استشهاد بكتاب 
|مؤلف= Laith Saadi 
|عنوان= Stealth Ciphers
|مسار= https://books.google.com/?id=Mll0WZAjdyEC&pg=PT170&dq=%22Mills%27+constant%22#v=onepage&q=%22Mills%27%20constant%22&f=false
|سنة= 2004
|ناشر= Trafford Publishing 
|isbn= 978-1-4120-2409-9
|صفحة= 160
| مسار أرشيف = https://web.archive.org/web/20200305205056/https://books.google.com/?id=Mll0WZAjdyEC&pg=PT170&dq=%22Mills'+constant%22#v=onepage&q=%22Mills'%20constant%22&f=false | تاريخ أرشيف = 5 مارس 2020 }}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\theta}</math>
||<math> \lfloor \theta^{3^{n}} \rfloor</math> primes
||<syntaxhighlight lang="mathematica">Nest[ NextPrime[#^3] &, 2, 7]^(1/3^8)</syntaxhighlight>
||
||{{OEIS2C|A051021}}
||[1;3,3,1,3,1,2,1,2,1,4,2,35,21,1,4,4,1,1,3,2,...]
||1947
||<small> 1.30637788386308069046861449260260571 </small> 
|-

<!----------------------------------------v--------------------------------------------->
|2.02988321281930725004
||عقدة الرقم 8 <ref>{{استشهاد بكتاب 
|مؤلف1=Jonathan Borwein |مؤلف2=David Bailey |عنوان= Mathematics by Experiment, 2nd Edition: Plausible Reasoning in the 21st Century
|مسار= https://books.google.com/?id=ysDiE0Enn4oC&pg=PA56&lpg=PA56&dq=2.029883212819307250042405108549#v=onepage&q=2.029883212819307250042405108549&f=false
|سنة= 2008
|ناشر= A K Peters, Ltd.
|isbn= 978-1-56881-442-1
|صفحة= 56
|مسار أرشيف= https://web.archive.org/web/20200304173038/https://books.google.com/?id=ysDiE0Enn4oC&pg=PA56&lpg=PA56&dq=2.029883212819307250042405108549#v=onepage&q=2.029883212819307250042405108549&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Blue Figure-Eight Knot.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>{V_{8}}</math>
||<math> 2 \sqrt{3}\, \sum_{n=1}^\infty \frac{1}{n
{2n \choose n}} \sum_{k=n}^{2n-1} \frac{1}{k} = 
6 \int \limits_{0}^{\pi / 3} 
\log \left( \frac{1}{2 \sin t} \right) \, dt = </math> 
<math>\scriptstyle
\frac{\sqrt{3}}{{9}}\, \sum \limits_{n=0}^\infty 
\frac{(-1)^n}{27^n}\,\left\{\!
\frac{{18}}{(6n+1)^2} - \frac{{18}}{(6n+2)^2} -
\frac{{24}}{(6n+3)^2} -
\frac{{6}}{(6n+4)^2} +
\frac{{2}}{(6n+5)^2}\!\right\}
</math>
||<syntaxhighlight lang="mathematica">6 integral[0 to pi/3]
 {log(1/(2 sin (n)))}</syntaxhighlight>
||
||{{OEIS2C|A091518}}
||[2;33,2,6,2,1,2,2,5,1,1,7,1,1,1,113,1,4,5,1,...]
||
||<small> 2.02988321281930725004240510854904057 </small> 
|-

<!------------------------------------------v------------------------------------------->
|262537412640768743.999999999999250073
||ثابت هيرميت-رامانوجان <ref>{{استشهاد بكتاب 
|مؤلف= L. J. Lloyd James Peter Kilford 
|عنوان= Modular Forms: A Classical and Computational Introduction
|مسار= https://books.google.com/?id=txPhITLO1YoC&pg=PA107&dq=262537412640768743.99999999999925#v=onepage&q=262537412640768743.99999999999925&f=false
|سنة= 2008  
|ناشر= Imperial College Press
|isbn= 978-1-84816-213-6
|صفحة= 107
|مسار أرشيف= https://web.archive.org/web/20200304173040/https://books.google.com/?id=txPhITLO1YoC&pg=PA107&dq=262537412640768743.99999999999925#v=onepage&q=262537412640768743.99999999999925&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{R}</math> 
||<math> e^{\pi\sqrt{163}}</math>
||<syntaxhighlight lang="mathematica">e^(π sqrt(163))</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A060295}}
||<small>[262537412640768743;1,1333462407511,1,8,1,1,5,...]</small>
||1859
||<small> 262537412640768743.999999999999250073 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|1.74540566240734686349 
||[[متوسط توافقي|المتوسط التوافقي]] خنشن <ref>{{استشهاد بكتاب 
|عنوان= Continued Fractions from Euclid till Present
|مسار= http://algo.inria.fr/seminars/sem98-99/vardi1-2.html#Finch95b
|سنة=  1998
|ناشر= IHES, Bures sur Yvette
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20161119040503/http://algo.inria.fr/seminars/sem98-99/vardi1-2.html | تاريخ أرشيف = 19 نوفمبر 2016 }}</ref>
||[[ملف:Plot harmonic mean.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>{K_{-1}}</math>
||<math> \frac {\log 2} {\sum \limits_{n=1}^\infty \frac {1}{n}
 \log\bigl(1{+}\frac{1}{n(n+2)}\bigr)} = \lim_{n \to \infty} \frac{n}{\frac{1}{a_1}+\frac{1}{a_2}+\cdots+\frac{1}{a_n}}</math>
''a''<sub>1</sub> ... ''a''<sub>''n''</sub> هي عناصر [[كسر مستمر]] [''a''<sub>0</sub>; ''a''<sub>1</sub>, ''a''<sub>2</sub>, ..., ''a''<sub>''n''</sub>]
||<syntaxhighlight lang="mathematica">(log 2)/
(sum[n=1 to ∞] 
{1/n log(1+
1/(n(n+2))}</syntaxhighlight>
||
||{{OEIS2C|A087491}}
||[1;1,2,1,12,1,5,1,5,13,2,13,2,1,9,1,6,1,3,1,...]
||
||<small> 1.74540566240734686349459630968366106 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|1.648721270700128146848
||[[جذر تربيعي|الجذر التربيعي]] للعدد [[ه (رياضيات)|ه]]<ref>{{استشهاد بكتاب 
|مؤلف= Julian Havil
|عنوان= The Irrationals: A Story of the Numbers You Can't Count On
|مسار= https://books.google.com/?id=BoqXQ87C-04C&pg=PA98&dq=1.6487212707#v=onepage&q=1.6487212707&f=false 
|سنة= 2012
|ناشر= Princeton University Press
|isbn= 978-0-691-14342-2
|صفحة= 98
|مسار أرشيف= https://web.archive.org/web/20200304173042/https://books.google.com/?id=BoqXQ87C-04C&pg=PA98&dq=1.6487212707#v=onepage&q=1.6487212707&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>\sqrt {e}</math>
||<math>\sum_{n = 0}^\infty \frac{1}{2^n n!} = \sum_{n = 0}^\infty \frac{1}{(2n)!!} = \frac{1}{1}+\frac{1}{2}+\frac{1}{8}+\frac{1}{48}+\cdots</math>
||<syntaxhighlight lang="mathematica">Sum[n=0 to ∞]
{1/(2^n n!)}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A019774}}
||[1;1,1,1,5,1,1,9,1,1,13,1,1,17,1,1,21,1,1,...] <br /> = [1;1,{{سطر فوقي|1,1,4p+1}}], p∈ℕ
||
||<small> 1.64872127070012814684865078781416357 </small>
|-

<!--------------------------------------------v----------------------------------------->
|1.017343061984449139714
||[[زيتا (توضيح)|زيتا]](6) <ref>{{استشهاد بكتاب 
|مؤلف=  Lennart R©Æde,Bertil Westergren 
|عنوان= Mathematics Handbook for Science and Engineering
|مسار= 
|سنة= 2004
|ناشر= Springer-Verlag 
|isbn= 3-540-21141-1
|صفحة= 194
}}</ref>
||[[ملف:Zeta.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>\zeta(6)</math>
||<math>\frac{\pi^6}{945} \! = \! \prod_{n=1}^\infty \! \underset{p_n: \text{ prime}}{ \frac{1}{{1-p_n}^{-6}}} = \frac{1}{1 \! -\! 2^{-6}} \! \cdot \! \frac{1}{1 \! - \! 3^{-6}}  \! \cdot \! \frac{1}{1 \! - \! 5^{-6}} \cdots</math>
||<syntaxhighlight lang="mathematica">Prod[n=1 to ∞]
{1/(1-ithprime
(n)^-6)}</syntaxhighlight> 
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A013664}}
||[1;57,1,1,1,15,1,6,3,61,1,5,3,1,6,1,3,3,6,1,...]
||
||<small> 1.01734306198444913971451792979092052 </small> 
|-

<!----------------------------------------v--------------------------------------------->
|0.108410151223111361511
||ثابت تروت <ref>{{استشهاد بكتاب 
|مؤلف=  Michael Trott
|عنوان= Finding Trott Constants
|مسار= http://www.mathematica-journal.com/issue/v10i2/contents/Corner10-2/Corner10-2.pdf 
|سنة=  
|ناشر= Wolfram Research
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20160303170712/http://www.mathematica-journal.com/issue/v10i2/contents/Corner10-2/Corner10-2.pdf | تاريخ أرشيف = 3 مارس 2016 }}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\mathrm{T}_1</math>
||<math> \textstyle [1, 0, 8, 4, 1, 0, 1, 5, 1, 2, 2, 3, 1, 1, 1, 3, 6,...]</math> <br/>
<math> \tfrac 1{1+\tfrac 1{0+\tfrac 1{8+\tfrac 1{4+\tfrac 1{1+\tfrac 1{0+1{/\cdots}}}}}}} </math>
||
||
||{{OEIS2C|A039662}}
||[0;9,4,2,5,1,2,2,3,1,1,1,3,6,1,5,1,1,2,...]
||
||<small> 0.10841015122311136151129081140641509</small> 
|-

<!------------------------------------------v------------------------------------------->
|0.0078749969978123844
||ثابت شاتان <ref>{{استشهاد بكتاب 
|مؤلف= David Darling 
|عنوان= The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes
|مسار= https://books.google.com/?id=HrOxRdtYYaMC&pg=PA63&dq=%22Chaitin+constant%22#v=onepage&q=%22Chaitin%20constant%22&f=false
|سنة= 2004
|ناشر= Wiley & Sons inc.
|isbn= 0-471-27047-4
|صفحة= 63
|مسار أرشيف= https://web.archive.org/web/20200304173044/https://books.google.com/?id=HrOxRdtYYaMC&pg=PA63&dq=%22Chaitin+constant%22#v=onepage&q=%22Chaitin%20constant%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<div style="text-align: center;">[[ملف:ProgramTree.svg|40px]]</div>
|bgcolor=#e0f0f0 align=center|<math>\Omega </math>
||<math>\sum_{p \in P} 2^{-|p|}</math>
||
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A100264}}
||[0; 126, 1, 62, 5, 5, 3, 3, 21, 1, 4, 1]
||1975
||0.0078749969978123844 
|-

<!-----------------------------------------v-------------------------------------------->
|0.83462684167407318628
||ثابت [[كارل فريدريش غاوس|جاووس]] <small>نص صغير</small><ref>{{استشهاد بكتاب 
|مؤلف1=Keith B. Oldham |مؤلف2=Jan C. Myland |مؤلف3=Jerome Spanier |عنوان= An Atlas of Functions: With Equator, the Atlas Function Calculator
|مسار= https://books.google.com/?id=UrSnNeJW10YC&pg=PA647&dq=%22Gauss%27s+constant%22#v=onepage&q=%22atlas%20is%20the%20Gauss%27s%20constant%22&f=false
|سنة= 2009  
|ناشر= Springer 
|isbn= 978-0-387-48806-6
|صفحة= 15
|مسار أرشيف= https://web.archive.org/web/20200304173046/https://books.google.com/?id=UrSnNeJW10YC&pg=PA647&dq=%22Gauss%27s+constant%22#v=onepage&q=%22atlas%20is%20the%20Gauss%27s%20constant%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{G}</math>
|| <math>  \frac{1}{\mathrm{agm}(1, \sqrt{2})} = \frac{4 \sqrt{2} \,(\tfrac14 !)^2}{\pi ^{3/2}}= \frac{2}{\pi}\int_0^1\frac{dx}{\sqrt{1 - x^4}}</math>
||<syntaxhighlight lang="mathematica">(4 sqrt(2)((1/4)!)^2)
/pi^(3/2)</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A014549}}
||[0;1,5,21,3,4,14,1,1,1,1,1,3,1,15,1,3,7,1,...]
||
||<small> 0.83462684167407318628142973279904680 </small> 
|-

<!---------------------------------------v---------------------------------------------->
|1.451369234883381050283
||ثابت [[يوهان جورج فون سولدنر|سولدنر]] [[سرينفاسا أينجار رامانجن|رامانجن]]<ref>{{استشهاد بكتاب
|مؤلف= Johann Georg Soldner
|عنوان= Théorie et tables d’une nouvelle fonction transcendante
|لغة= fr
|مسار= https://books.google.de/?id=g4Q_AAAAcAAJ&pg=PA42
|سنة= 1809
|ناشر= J. Lindauer, München
|صفحة= 42
|مسار أرشيف= https://web.archive.org/web/20200614041720/https://books.google.de/books?id=g4Q_AAAAcAAJ&pg=PA42&hl=de|تاريخ أرشيف=2020-03-04}}</ref><ref>{{استشهاد بكتاب
|مؤلف= Lorenzo Mascheroni
|عنوان= Adnotationes ad calculum integralem Euleri
|لغة= latin
|مسار= https://books.google.com/?id=XkgDAAAAQAAJ&pg=RA1-PA17
|سنة= 1792
|ناشر= Petrus Galeatius, Ticini
|صفحة= 17
|مسار أرشيف= https://web.archive.org/web/20200304173050/https://books.google.com/?id=XkgDAAAAQAAJ&pg=RA1-PA17|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Integrallogrithm.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>{\mu}</math>
||<math> \mathrm{li} (x) = \int\limits_0^x  \frac{dt}{\ln t} = 0  
{\color{White}{......}} </math> li = [[لوغاريتم|لوغارتم]] خطي <br/>
<math> \mathrm{li}(x)\;=\;\mathrm{Ei}(\ln{x})  
{\color{White}{........}} </math> Ei = [[تكامل أسي]]
||<syntaxhighlight lang="mathematica">FindRoot[li(x) = 0]</syntaxhighlight>
|'''[[عدد غير كسري|غ.ك]]'''
||{{OEIS2C|A070769}}
||[1;2,4,1,1,1,3,1,1,1,2,47,2,4,1,12,1,1,2,2,1,...]
||1792 <br /> to <br /> 1809
||<small> 1.45136923488338105028396848589202744 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|0.64341054628833802618
||ثابت الكاهن <ref>{{استشهاد بكتاب 
|مؤلف= Yann Bugeaud
|عنوان= Series representations for some mathematical constants
|مسار= https://books.google.com/?id=iAg8FL5jKSgC&pg=PA72&dq=%22cahen+constant%22#v=onepage&q=%22cahen%20constant%22&f=false
|سنة= 2004
|ناشر= 
|isbn= 0-521-82329-3
|صفحة= 72
|مسار أرشيف= https://web.archive.org/web/20200304173052/https://books.google.com/?id=iAg8FL5jKSgC&pg=PA72&dq=%22cahen+constant%22#v=onepage&q=%22cahen%20constant%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\xi _{2}</math>
||<math> \sum_{k=1}^{\infty} \frac{(-1)^{k}}{s_k-1} = \frac{1}{1} - \frac{1}{2} + \frac{1}{6} - \frac{1}{42} + \frac{1}{1806} {\,\pm \cdots}  </math> 
<br/> <math>\, \, S_0= \, 2 , \,\, S_k= \, 1+\prod \limits_{n=0}^{k-1} S_n\text{ for}\;k>0 </math>
||
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A080130}}
||[0; 1, 1, 1, 4, 9, 196, 16641, 639988804, ...]
||1891
|<small> 0.64341054628833802618225430775756476 </small> 
|-

<!------------------------------------------v------------------------------------------->
| 1.414213562373095048801
||[[الجذر التربيعي ل 2]]، ثابت [[فيثاغورس]] .<ref>{{استشهاد بكتاب 
|مؤلف= Calvin C Clawson 
|عنوان= Mathematical sorcery: revealing the secrets of numbers
|مسار= https://books.google.com/?id=sPRbZACsXogC&pg=PA293&dq=pi+nested+radical#v=snippet&q=%22Again%20we%20have%20an%20amazing%20expression.%22&f=false
|سنة=  2001
|ناشر= 
|isbn= 978 0 7382 0496-3
|صفحة= IV
| مسار أرشيف = https://web.archive.org/web/20200414175148/https://books.google.com/?id=sPRbZACsXogC&pg=PA293&dq=pi+nested+radical#v=snippet&q=%22Again%20we%20have%20an%20amazing%20expression.%22&f=false | تاريخ أرشيف = 14 أبريل 2020 }}</ref>
||[[ملف:Square root of 2 triangle.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>\sqrt{2}</math>
||<math>\! \prod_{n=1}^\infty \! \left( 1 \! + \! \frac{(-1)^{n+1}}{2n-1} \right) \! = \! \left(1 \! + \! \frac{1}{1}\right) \! \left(1 \! - \! \frac{1}{3} \right) \! \left(1 \! + \! \frac{1}{5} \right) \cdots </math>
||<syntaxhighlight lang="mathematica">prod[n=1 to ∞] 
 {1+(-1)^(n+1) 
 /(2n-1)}</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A002193}}
||[1;2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,...]<br /> = [1;{{سطر فوقي|2}}...]
||
||<small> 1.41421356237309504880168872420969808 </small> 
|-

<!------------------------------------------v------------------------------------------->
|1.77245385090551602729
||ثابت كارلسون ليفين <ref name="books.google.com"/>
||
|bgcolor=#e0f0f0 align=center|<math>{\Gamma}(\tfrac12)</math>
||<math>\sqrt{\pi} = \left(-\frac{1}{2}\right)! = \int_{-\infty }^{\infty } \frac {1}{e^{x^2}} \, dx  = \int_{0 }^{1} \frac {1}{\sqrt{-\ln x}} \, dx </math> 
||<syntaxhighlight lang="mathematica">sqrt (pi)</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A002161}}
||[1;1,3,2,1,1,6,1,28,13,1,1,2,18,1,1,1,83,1,...]
||
||<small> 1.77245385090551602729816748334114518 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|1.05946309435929526456
||الفاصل الموسيقي بين نصف كل نغمة<ref>{{استشهاد بكتاب 
|مؤلف= Bart Snapp 
|عنوان= Numbers and Algebra
|مسار= https://people.math.osu.edu/snapp.14/1165/NumbersAlgebra.pdf
|سنة= 2012
| مسار أرشيف = https://web.archive.org/web/20130927170233/http://www.math.osu.edu/~snapp.14/1165/NumbersAlgebra.pdf | تاريخ أرشيف = 27 سبتمبر 2013 }}</ref><ref>{{استشهاد بكتاب 
|مؤلف= George Gheverghese Joseph 
|عنوان= The Crest of the Peacock: Non-European Roots of Mathematics
|مسار= https://books.google.com/?id=ymud91nTc9YC&pg=PA295&dq=1.059463094359295264561825#v=onepage&q=1.059463094359295264561825&f=false
|سنة= 2011  
|ناشر= Princeton University Press
|isbn= 978-0-691-13526-7
|صفحة= 295
|مسار أرشيف= https://web.archive.org/web/20200304173055/https://books.google.com/?id=ymud91nTc9YC&pg=PA295&dq=1.059463094359295264561825#v=onepage&q=1.059463094359295264561825&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Rast scale.svg|100px]]
[[ملف:YB0214 Clavier tempere.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>\sqrt[12]{2}</math>
||<math>
\begin{array}{l|ccccccccccccr}
\! 2^\frac{x}{12} \! & \!\!\scriptstyle{0} & \!\!\!\!\scriptstyle{1} & \!\!\scriptstyle{2} & \!\!\scriptstyle{3}
 & \!\!\scriptstyle{4} & \scriptstyle{5} & \!\!\scriptstyle{6} & \!\!\scriptstyle{7} & \!\!\scriptstyle{8}
 & \!\!\scriptstyle{9} & \!\! \scriptstyle{10} & \!\! \scriptstyle{11} & \!\! \scriptstyle{12} \\
\hline
\! \scriptstyle{\textrm{Key}} \! & \!\scriptstyle{\mathrm{C_1}} & \!\!\scriptstyle{\mathrm{C^\#}} & \!\!\scriptstyle{\mathrm{D}} 
 & \!\scriptstyle{\mathrm{D^\#}} & \!\!\scriptstyle{\mathrm{E}} & \scriptstyle{\mathrm{F}} & \!\scriptstyle{\mathrm{F^\#}}
 & \!\!\scriptstyle{\mathrm{G}} & \!\scriptstyle{\mathrm{G^\#}} & \!\!\scriptstyle{\mathrm{A}} & \!\scriptstyle{\mathrm{A^\#}} 
 & \!\!\scriptstyle{\mathrm{B}} & \!\scriptstyle{\mathrm{C_2}}
\end{array}
</math>(A = 440&nbsp;Hz)
||<syntaxhighlight lang="mathematica">2^(1/12)</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A010774}}
||[1;16,1,4,2,7,1,1,2,2,7,4,1,2,1,60,1,3,1,2,...]
||
||<small> 1.05946309435929526456182529494634170 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|1.01494160640965362502
||ثابت جيسكنج <ref>{{استشهاد بكتاب 
|مؤلف= Steven Finch
|عنوان= Volumes of Hyperbolic 3-Manifolds
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/hyp.pdf
|سنة=  
|ناشر= Harvard University
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20160419150522/http://www.people.fas.harvard.edu/~sfinch/csolve/hyp.pdf | تاريخ أرشيف = 19 أبريل 2016 }}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\pi \ln \beta} </math>
||<math>\frac{3\sqrt{3}}{4} \left(1- \sum_{n=0}^\infty \frac{1}{(3n+2)^2}+ \sum_{n=1}^\infty\frac{1}{(3n+1)^2} \right)= </math> <br/> 
<math>\textstyle \frac{3\sqrt{3}}{4} \left( 1 - \frac{1}{2^2} + \frac{1}{4^2}-\frac{1}{5^2}+\frac{1}{7^2}-\frac{1}{8^2}+\frac{1}{10^2} \pm \cdots \right)</math>.
||<syntaxhighlight lang="mathematica">sqrt(3)*3/4 *(1
-Sum[n=0 to ∞]
{1/((3n+2)^2)}
+Sum[n=1 to ∞]
{1/((3n+1)^2)})</syntaxhighlight>
||
||{{OEIS2C|A143298}}
||[1;66,1,12,1,2,1,4,2,1,3,3,1,4,1,56,2,2,11,...]
||1912
||<small> 1.01494160640965362502120255427452028 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|2.62205755429211981046
||ثابت ليمنيسكاتي <ref>{{استشهاد بكتاب 
|مؤلف1=J. Coates |مؤلف2=Martin J. Taylor |عنوان= L-Functions and Arithmetic
|مسار= https://books.google.com/?id=aKQhpm1h770C&pg=PA333&dq=2.6220575#v=onepage&q&f=false
|سنة= 1991 
|ناشر= Cambridge University Press
|isbn= 0-521-38619-5
|صفحة= 333
|مسار أرشيف= https://web.archive.org/web/20200304173057/https://books.google.com/?id=aKQhpm1h770C&pg=PA333&dq=2.6220575#v=onepage&q&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Lemniscate of Gerono.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{\varpi} </math>
||<math> \pi \, {G} = 4 \sqrt{\tfrac2\pi}\,\Gamma{\left(\tfrac54 \right)^2} = \tfrac14 \sqrt{\tfrac{2}{\pi}}\,\Gamma {\left(\tfrac14 \right)^2} = 4 \sqrt{\tfrac2\pi}\left(\tfrac14 !\right)^2</math>
|| <syntaxhighlight lang="mathematica">4 sqrt(2/pi)
((1/4)!)^2</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A062539}}
||[2;1,1,1,1,1,4,1,2,5,1,1,1,14,9,2,6,2,9,4,1,...]
||1798
||<small> 2.62205755429211981046483958989111941 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|1.28242712910062263687
||ثابت [[جيمس يتبريد لي جلايشر|جلايشر]] كين كيلن
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>{A}</math>
||<math> e^{\frac{1}{12}-\zeta^\prime(-1)} =
 e^{\frac{1}{8}-\frac{1}{2}\sum\limits_{n=0}^\infty \frac{1}{n+1} \sum\limits_{k=0}^n \left(-1\right)^k \binom{n}{k} \left(k+1\right)^2 \ln(k+1)}</math>
||<syntaxhighlight lang="mathematica">e^(1/12-zeta´{-1})</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A074962}}
||[1;3,1,1,5,1,1,1,3,12,4,1,271,1,1,2,7,1,35,...]
||
||<small> 1.28242712910062263687534256886979172 </small> 
|-

<!------------------------------------------v------------------------------------------->
|4.227453533376265408-
||دالة دي جاما (1/4) <ref>{{استشهاد بكتاب 
|مؤلف1=Horst Alzera |مؤلف2=Dimitri Karayannakisb |مؤلف3=H.M. Srivastava |عنوان= Series representations for some mathematical constants
|مسار= https://www.sciencedirect.com/science/article/pii/S0022247X05005883
|سنة=  2005
|ناشر= Elsevier Inc 
|isbn= 
|صفحة= 149
| مسار أرشيف = https://web.archive.org/web/20170402131857/http://www.sciencedirect.com/science/article/pii/S0022247X05005883 | تاريخ أرشيف = 2 أبريل 2017 }}</ref>
||[[ملف:Complex Polygamma 0.jpg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{\psi} (\tfrac14) </math>
|| <math>  -\gamma -\frac{\pi}{2} - 3\ln{2} = -\gamma+\sum_{n=0}^{\infty}\left(\frac{1}{n+1}-\frac{1}{n+\tfrac14}\right)</math>
||<syntaxhighlight lang="mathematica">-EulerGamma 
-\pi/2 -3 log 2</syntaxhighlight>
||
||{{OEIS2C|A020777}}
||-[4;4,2,1,1,10,1,5,9,11,1,22,1,1,14,1,2,1,4,...]
||
||<small> -4.2274535333762654080895301460966835 </small> 
|-

<!------------------------------------------v------------------------------------------->
| 0.286747428434478734107
||ثابت الإهمال القوي<ref>{{استشهاد بكتاب 
|مؤلف= Steven R. Finch 
|عنوان= Quadratic Dirichlet L-Series
|مسار= http://www.people.fas.harvard.edu/~sfinch/csolve/ls.pdf
|سنة= 2005 
|ناشر= 
|isbn= 
|صفحة= 12
| مسار أرشيف = https://web.archive.org/web/20160303211742/http://www.people.fas.harvard.edu/~sfinch/csolve/ls.pdf | تاريخ أرشيف = 3 مارس 2016 }}</ref>
||<br /><br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>K_{2}</math>
||<math> \prod_{n=1}^\infty \underset{p_n: \text{ prime}} {\left( 1-\frac{3 p_n-2}{{p_n}^{3}}\right)} = \frac {6}{\pi ^2}\prod_{n=1}^\infty \underset{p_n: \text{ prime}} {\left( 1-\frac{1}{{p_n(p_n+1)}}\right)} </math> 
||<syntaxhighlight lang="mathematica">N[ prod[k=1 to ∞] 
 {1-(3*prime(k)-2) 
 /(prime(k)^3)}]</syntaxhighlight>
||
||{{OEIS2C|A065473}}
||[0;3,2,19,3,12,1,5,1,5,1,5,2,1,1,1,1,1,3,7,...]
||
||<small> 0.28674742843447873410789271278983845 </small> 
|-

<!----------------------------------------v--------------------------------------------->
| 3.62560990822190831193
||[[غاما (توضيح)|جاما]](1/4)<ref>{{استشهاد بكتاب 
|مؤلف= Refaat El Attar 
|عنوان= Special Functions And Orthogonal Polynomials
|مسار= https://books.google.com/?id=r3Zj__Ag7LwC&pg=PA58&dq=3.6256#v=onepage&q=3.6256&f=false
|سنة= 2006 
|ناشر= Lulu Press
|isbn= 1-4116-6690-9
|صفحة= 58
|مسار أرشيف= https://web.archive.org/web/20200304172832/https://books.google.com/books?id=r3Zj__Ag7LwC&pg=PA58&dq=3.6256&hl=en#v=onepage&q=3.6256&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Gamma abs 3D.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>\Gamma(\tfrac14)</math>
||<math> 4 \left(\frac{1}{4}\right)! = \left(-\frac{3}{4}\right)! </math>
||<syntaxhighlight lang="mathematica">4(1/4)!</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A068466}}
||[3;1,1,1,2,25,4,9,1,1,8,4,1,6,1,1,19,1,1,4,1,...]
||1729
||<small> 3.62560990822190831193068515586767200 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|1.66168794963359412129
||ثابت سموس <ref>{{استشهاد بدورية محكمة
|مؤلف1=Jesus Guillera  |مؤلف2=Jonathan Sondow
|عنوان= Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent
|صحيفة=The Ramanujan Journal
|المجلد=16 |العدد=3 |صفحات=247–270
|arxiv=math/0506319
|سنة=2005
|doi=10.1007/s11139-007-9102-0
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\sigma}</math>
||<math>\prod_{n=1}^\infty n^{{1/2}^n} = \sqrt {1 \sqrt {2 \sqrt{3 \cdots}}} = 1^{1/2} \; 2^{1/4} \; 3^{1/8} \cdots </math> 
||<syntaxhighlight lang="mathematica">prod[n=1 to ∞]
{n ^(1/2)^n}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A065481}}
||[1;1,1,1,21,1,1,1,6,4,2,1,1,2,1,3,1,13,13,...]
||
||<small> 1.66168794963359412129581892274995074 </small> 
|-

<!-----------------------------------------v-------------------------------------------->
| 0.955316618124509278163
||الزاوية السحرية <ref>{{استشهاد بكتاب 
|مؤلف= Andras Bezdek
|عنوان= Discrete Geometry
|مسار= https://books.google.com/?id=WoaxgpHu19gC&pg=PA150&lpg=PA150&dq=0.955316#v=onepage&q=0.955316&f=false
|سنة= 2003
|ناشر= Marcel Dekkcr, Inc.
|isbn= 0-8247-0968-3
|صفحة= 150
|مسار أرشيف= https://web.archive.org/web/20200304173059/https://books.google.com/?id=WoaxgpHu19gC&pg=PA150&lpg=PA150&dq=0.955316#v=onepage&q=0.955316&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Magic angle.png|100px]]
|bgcolor=#e0f0f0 align=center|<math> {\theta_m} </math>
||<math> \arctan \left(\sqrt{2}\right) = \arccos \left(\sqrt{\tfrac13}\right) \approx   \textstyle {54.7356} ^{ \circ } </math>
||<syntaxhighlight lang="mathematica">arctan(sqrt(2))</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A195696}}
||[0;1,21,2,1,1,1,2,1,2,2,4,1,2,9,1,2,1,1,1,3,...]
||
||<small> 0.95531661812450927816385710251575775 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|1.78107241799019798523
|| دالة بارنس <ref>{{استشهاد بكتاب 
|مؤلف1=H. M. Srivastava |مؤلف2=Junesang Choi |عنوان= Zeta and q-Zeta Functions and Associated Series and Integrals
|مسار= https://books.google.com/?id=DUyACqwqaqIC&pg=PA613&dq=%22Barnes+G-Function%22#v=onepage&q=%22generalized%20Barnes%20G-function%22&f=false
|سنة= 2012  
|ناشر= Elsevier
|isbn= 978-0-12-385218-2
|صفحة= 613
|مسار أرشيف= https://web.archive.org/web/20200614202008/https://books.google.com/books?id=DUyACqwqaqIC&pg=PA613&dq=%22Barnes+G-Function%22&hl=en#v=onepage&q=%22generalized%20Barnes%20G-function%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>e^{\gamma} </math>
||<math>\prod_{n=1}^\infty \frac{e^{\frac{1}{n}}}{1+\tfrac1n} = \prod_{n=0}^\infty \left(\prod_{k=0}^n (k+1)^{(-1)^{k+1}{n \choose k}}\right)^{\frac{1}{n+1}} = </math>
<math>\textstyle \left (\frac{2}{1} \right )^{1/2} \left (\frac{2^2}{1 \cdot 3} \right )^{1/3} \left (\frac{2^3 \cdot 4}{1 \cdot 3^3} \right )^{1/4}
\left (\frac{2^4 \cdot 4^4}{1 \cdot 3^6 \cdot 5} \right )^{1/5}\cdots </math>
||<syntaxhighlight lang="mathematica">Prod[n=1 to ∞]
{e^(1/n)}
/{1 + 1/n}</syntaxhighlight>
||
||{{OEIS2C|A073004}}
||[1;1,3,1,1,3,5,4,1,1,2,2,1,7,9,1,16,1,1,1,2,...]
||
||<small> 1.78107241799019798523650410310717954 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|0.74759792025341143517
||ثابت رينيه لركن السيارات <ref>{{استشهاد بكتاب 
|مؤلف= Weisstein, Eric W
|عنوان= Rényi's Parking Constants
|مسار= http://mathworld.wolfram.com/RenyisParkingConstants.html
|سنة=  
|ناشر= MathWorld
|isbn= 
|صفحة= (4)
| مسار أرشيف = https://web.archive.org/web/20190826122505/http://mathworld.wolfram.com/RenyisParkingConstants.html | تاريخ أرشيف = 26 أغسطس 2019 }}</ref>
||[[ملف:Random car parking problem.svg|100px]] [[ملف:ParallelParkingAnimation2.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math>{m}</math>
||<math> \int \limits_{0}^{\infty} exp \left(\! -2 \int \limits_{0}^{x} \frac {1-e^{-y}}{y} dy\right)\! dx = {e^{-2 \gamma}} \int \limits_{0}^{\infty} \frac{e^{-2 \Gamma(0,n)}}{n^2} </math> 
||<syntaxhighlight lang="mathematica">[e^(-2*Gamma)] 
* Int{n,0,∞}[ e^(- 2
*Gamma(0,n)) /n^2]</syntaxhighlight>
||
||{{OEIS2C|A050996}}
||[0;1,2,1,25,3,1,2,1,1,12,1,2,1,1,3,1,2,1,43,...]
||
||<small> 0.74759792025341143517873094383017817 </small> 
|-

<!------------------------------------------v------------------------------------------->
|1.273239544735162686151
||سلسلة رامانوجان-فورسيث <ref>{{استشهاد بكتاب 
|مؤلف= H. K. Kuiken
|عنوان= Practical Asymptotics
|مسار= https://books.google.com/?id=r_-4OQ2CVY8C&pg=PA162&dq=1.2732395#v=onepage&q=1.2732395&f=false
|سنة= 2001 
|ناشر= KLUWER ACADEMIC PUBLISHERS
|isbn= 0-7923-6920-3
|صفحة= 162
|مسار أرشيف= https://web.archive.org/web/20200304173106/https://books.google.com/?id=r_-4OQ2CVY8C&pg=PA162&dq=1.2732395#v=onepage&q=1.2732395&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\frac {4}{\pi}</math>
||<math> \displaystyle \sum \limits_{n=0}^\infty \textstyle \left(\frac{(2n-3)!!}{(2n)!!}\right)^2 = {1  \! +  \!  \left(\frac {1}{2} \right)^2  \! + \! \left(\frac {1}{2 \cdot 4} \right)^2 \! + \! \left(\frac {1 \cdot 3}{2 \cdot 4 \cdot 6} \right)^2 + \cdots}</math>
||<syntaxhighlight lang="mathematica">Sum[n=0 to ∞] 
 {[(2n-3)!! 
 /(2n)!!]^2}</syntaxhighlight>
|'''[[عدد غير كسري|غ.ك]]'''
||{{OEIS2C|A088538}}
||[1;3,1,1,1,15,2,72,1,9,1,17,1,2,1,5,1,1,10,...]
||
||<small> 1.27323954473516268615107010698011489 </small> 
|-

<!-------------------------------------------v------------------------------------------>
| 1.444667861009766133658
||عدد ستينر، [[ه (رياضيات)|ه]] [[جذر (توضيح)|جذر]] [[ه (رياضيات)|ه]] <ref>{{استشهاد بكتاب 
|مؤلف= Eli Maor
|عنوان= e: The Story of a Number
|مسار= https://books.google.com/?id=dSfaaVccJ_UC&pg=PA51&lpg=PA51&dq=1.444667861#v=onepage&q=1.444667861&f=false
|سنة= 2006
|ناشر= Princeton University Press
|isbn= 0-691-03390-0
|مسار أرشيف= https://web.archive.org/web/20200304173109/https://books.google.com/books?id=dSfaaVccJ_UC&pg=PA51&lpg=PA51&dq=1.444667861&hl=en#v=onepage&q=1.444667861&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<div style="text-align: center;">[[ملف:Infinite power tower.svg|80px]]</div>
|bgcolor=#e0f0f0 align=center|<math>\sqrt[e]{e}</math>
||<math>e^{\frac{1}{e}}{\color{White}{...........}}</math> 
||<syntaxhighlight lang="mathematica">e^(1/e)</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A073229}}
||[1;2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]
||
||<small> 1.44466786100976613365833910859643022 </small> 
|-

<!-----------------------------------------v-------------------------------------------->
|0.692200627555346353865
||الحد الأدنى للدالة <br/> '''ƒ'''(x) = x<sup>x</sup> <ref>{{استشهاد بكتاب 
|مؤلف= Clifford A. Pickover
|عنوان= A Passion for Mathematics
|مسار= https://books.google.com/?id=03CVDsZSBIcC&pg=PA387&dq=Clifford+A.Pickover+%22A+passion+for+mathematics%22+0.692200#v=onepage&q=Clifford%20A.Pickover%20%22A%20passion%20for%20mathematics%22%200.692200&f=false
|سنة= 2005
|ناشر= John Wiley & Sons, Inc.
|isbn= 0-471-69098-8
|صفحة= 90
|مسار أرشيف= https://web.archive.org/web/20200304173111/https://books.google.com/books?id=03CVDsZSBIcC&pg=PA387&dq=Clifford+A.Pickover+%22A+passion+for+mathematics%22+0.692200&hl=en#v=onepage&q=Clifford%20A.Pickover%20%22A%20passion%20for%20mathematics%22%200.692200&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math> {\left(\frac{1}{e}\right)}^\frac{1}{e}</math>
||<math>{e}^{-\frac{1}{e}} {\color{White}{..........}}</math> = مقلوب عدد ستينر 
||<syntaxhighlight lang="mathematica">e^(-1/e)</syntaxhighlight>
||
||{{OEIS2C|A072364}}
||[0;1,2,4,55,27,1,1,16,9,3,2,8,3,2,1,1,4,1,9,...]
||
|<small> 0.69220062755534635386542199718278976 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|0.34053732955099914282
||ثابت [[سير عشوائي|السير العشوائي]] <ref>{{استشهاد بكتاب 
|مؤلف= Steven R. Finch
|عنوان= Mathematical Constants
|مسار= https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA322&dq=%22P%C3%B3lya+Random+Walk%22+finch#v=onepage&q=%22P%C3%B3lya%20Random%20Walk%22%20finch&f=false
|سنة= 2003 
|ناشر= Cambridge University Press
|isbn= 3-540-67695-3
|صفحة= 322
|مسار أرشيف= https://web.archive.org/web/20200304172835/https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA322&dq=%22P%C3%B3lya+Random+Walk%22+finch#v=onepage&q=%22P%C3%B3lya%20Random%20Walk%22%20finch&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Walk3d 0.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>{p(3)}</math>
||<math> 1- \!\!\left({3\over(2\pi)^3}\int\limits_{-\pi}^{\pi} \int\limits_{-\pi}^{\pi} \int\limits_{-\pi}^{\pi} {dx\,dy\,dz\over 3-\!\cos x-\!\cos y-\!\cos z}\right)^{\!-1}</math>
<math> = 1- 16\sqrt{\tfrac23}\;\pi^3 \left(\Gamma(\tfrac{1}{24})\Gamma(\tfrac{5}{24})\Gamma(\tfrac{7}{24})\Gamma(\tfrac{11}{24})\right)^{-1}</math>
||<syntaxhighlight lang="mathematica">1-16*Sqrt[2/3]*Pi^3 
/(Gamma[1/24]
*Gamma[5/24]
*Gamma[7/24]
*Gamma[11/24])</syntaxhighlight>
||
||{{OEIS2C|A086230}}
||[0;2,1,14,1,3,8,1,5,2,7,1,12,1,5,59,1,1,1,3,...]
||
||<small> 0.34053732955099914282627318443290289 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|0.543258965342976706952
||نظرية بلوتش (المتغيرات المركبة) <ref>{{استشهاد بكتاب 
|مؤلف= Eric W. Weisstein
|عنوان= CRC Concise Encyclopedia of Mathematics, Second Edition
|مسار= https://books.google.com/?id=aFDWuZZslUUC&pg=PA1688&dq=Bloch-Landau+constant#v=onepage&q=Bloch-Landau%20constant&f=false 
|سنة= 2003
|ناشر= CRC Press
|isbn= 1-58488-347-2
|صفحة= 1688
|مسار أرشيف= https://web.archive.org/web/20200304172837/https://books.google.com/?id=aFDWuZZslUUC&pg=PA1688&dq=Bloch-Landau+constant#v=onepage&q=Bloch-Landau%20constant&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{L}</math>
||<math> = \frac {\Gamma(\tfrac13)\;\Gamma(\tfrac{5}{6})} {\Gamma(\tfrac{1}{6})} = \frac {(-\tfrac23)!\;(-1+\tfrac56)!} {(-1+\tfrac16)!}</math>
||<syntaxhighlight lang="mathematica">gamma(1/3)
*gamma(5/6)
/gamma(1/6)</syntaxhighlight>
||
||{{OEIS2C|A081760}}
||[0;1,1,5,3,1,1,2,1,1,6,3,1,8,11,2,1,1,27,4,...]
||1929
||<small> 0.54325896534297670695272829530061323 </small> 
|-

<!----------------------------------------v-------------------------------------------->
|0.187859642462067120248
||ثابت إم أر بي (مارفن راي بيرنز) <ref>{{استشهاد بكتاب
|مؤلف= Richard E. Crandall
|عنوان= Unified algorithms for polylogarithm, L-series, and zeta variants
|مسار= http://www.perfscipress.com/papers/UniversalTOC25.pdf
|سنة= 2012
|ناشر= perfscipress.com
|مسار أرشيف= https://web.archive.org/web/20200618000627/https://web.archive.org/web/20130430193005/http://www.perfscipress.com/papers/UniversalTOC25.pdf
|تاريخ أرشيف= 18 يونيو 2020
|تاريخ الوصول= 5 سبتمبر 2019
|حالة المسار= bot: unknown
}}</ref><ref>{{استشهاد بأرخايف 
|مؤلف= RICHARD J. MATHAR
|عنوان= NUMERICAL EVALUATION OF THE OSCILLATORY INTEGRAL OVER exp(I pi  x)x^1/x BETWEEN 1 AND INFINITY
|arxiv= 0912.3844
|سنة= 2010
|class=math.CA
}}</ref><ref>{{استشهاد بكتاب 
|مؤلف= M.R.Burns
|عنوان= Root constant
|مسار= http://marvinrayburns.com/Original_MRB_Post.html
|سنة= 1999
|ناشر= Marvin Ray Burns
| مسار أرشيف = https://web.archive.org/web/20190829130105/http://marvinrayburns.com/Original_MRB_Post.html | تاريخ أرشيف = 29 أغسطس 2019 }}</ref>
||[[ملف:MRB-Gif.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math> C_{{}_{MRB}}</math>
||<math> \sum_{n=1}^{\infty} (-1)^n (n^{1/n}-1) =  - \sqrt[1]{1} + \sqrt[2]{2} - \sqrt[3]{3} + \cdots</math>
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞]
{(-1)^n (n^(1/n)-1)}</syntaxhighlight> 
||
||{{OEIS2C|A037077}}
||[0;5,3,10,1,1,4,1,1,1,1,9,1,1,12,2,17,2,2,1,...]
||1999
||<small> 0.18785964246206712024851793405427323 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|1.4670780794339754728977
||ثابت بورتر<ref>{{استشهاد بكتاب 
|مؤلف= Michel A. Théra
|عنوان= Constructive, Experimental, and Nonlinear Analysis
|مسار= https://books.google.com/?id=QTcCSegK6jQC&pg=PA80&dq=%22Porter%E2%80%99s+constant%22#v=onepage&q=%22Porter%E2%80%99s%20constant%22&f=false
|سنة= 2002 
|ناشر= CMS-AMS
|isbn= 0-8218-2167-9
|صفحة= 77
|مسار أرشيف= https://web.archive.org/web/20200304173113/https://books.google.com/?id=QTcCSegK6jQC&pg=PA80&dq=%22Porter%E2%80%99s+constant%22#v=onepage&q=%22Porter%E2%80%99s%20constant%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{C}</math>
||<math> \frac{6\ln 2}{\pi ^2} \left(3 \ln 2 + 4 \,\gamma -\frac{24}{\pi ^2} \,\zeta '(2)-2 \right)-\frac{1}{2}</math> 
<math> \scriptstyle \gamma \, \text{= Euler–Mascheroni Constant} = 0.5772156649\ldots </math>
<math> \scriptstyle \zeta '(2) \,\text{= Derivative of }\zeta(2)= 
- \sum \limits_{n = 2}^{\infty} \frac{\ln n}{n^2} = -0.9375482543\ldots </math>
|| <syntaxhighlight lang="mathematica">6*ln2/pi^2(3*ln2+ 
4 EulerGamma- 
WeierstrassZeta'(2) 
*24/pi^2-2)-1/2</syntaxhighlight> 
||
||{{OEIS2C|A086237}}
||[1;2,7,10,1,2,38,5,4,1,4,12,5,1,5,1,2,3,1,...]
||1974
||<small> 1.46707807943397547289779848470722995 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|4.66920160910299067185
||ثابت [[ميتشل فايينبوم|فايينبوم]] δ <ref>{{استشهاد بكتاب 
|مؤلف= Kathleen T. Alligood
|عنوان= Chaos: An Introduction to Dynamical Systems
|مسار= https://books.google.com/?id=i633SeDqq-oC&pg=PA500&dq=669201609#v=onepage&q=669201609&f=false
|سنة= 1996  
|ناشر= Springer
|isbn= 0-387-94677-2
|مسار أرشيف= https://web.archive.org/web/20200304173116/https://books.google.com/?id=i633SeDqq-oC&pg=PA500&dq=669201609#v=onepage&q=669201609&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:LogisticMap BifurcationDiagram.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>{\delta}</math>
||<math> \lim_{n \to \infty}\frac {x_{n+1}-x_n}{x_{n+2}-x_{n+1}} \qquad \scriptstyle x \in (3.8284;\, 3.8495)</math>
<math> \scriptstyle x_{n+1}=\,ax_n(1-x_n)\quad \text{or} \quad x_{n+1}=\,a\sin(x_n)</math>
||
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A006890}}
||[4;1,2,43,2,163,2,3,1,1,2,5,1,2,3,80,2,5,...]
||1975
||<small> 4.66920160910299067185320382046620161 </small> 
|-

<!------------------------------------------v------------------------------------------->
| 2.50290787509589282228
||ثابت [[ميتشل فايينبوم|فايينبوم]] α<ref>{{استشهاد بكتاب 
|مؤلف1=K. T. Chau |مؤلف2=Zheng Wang |عنوان= Chaos in Electric Drive Systems: Analysis, Control and Application
|مسار= https://books.google.com/?id=DhCbYXzLFLsC&pg=PA7&dq=2.502907875095892822283902873218#v=onepage&q=2.502907875095892822283902873218&f=false
|سنة= 201  
|ناشر= John Wiley & Son
|isbn= 978-0-470-82633-1
|صفحة= 7 
|مسار أرشيف= https://web.archive.org/web/20200304173118/https://books.google.com/?id=DhCbYXzLFLsC&pg=PA7&dq=2.502907875095892822283902873218#v=onepage&q=2.502907875095892822283902873218&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Mandelbrot zoom.gif|100px]]
|bgcolor=#e0f0f0 align=center|<math>\alpha</math>
||<math>\lim_{n \to \infty}\frac {d_n}{d_{n+1}}</math>
||
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A006891}}
||[2;1,1,85,2,8,1,10,16,3,8,9,2,1,40,1,2,3,...]
||1979
||<small> 2.50290787509589282228390287321821578 </small> 
|-

<!----------------------------------------------v--------------------------------------->
| 0.62432998854355087099
||ثابت غولومب-ديكمان <ref>{{استشهاد بكتاب 
|مؤلف= Eric W. Weisstein
|عنوان= CRC Concise Encyclopedia of Mathematics
|مسار= https://books.google.com/?id=aFDWuZZslUUC&pg=PA1211&lpg=PA1211&dq=Golomb%E2%80%93Dickman+constant#v=onepage&q=Golomb%E2%80%93Dickman%20constant&f=false
|سنة= 2002
|ناشر= Crc Press
|isbn= 
|صفحة= 1212
|مسار أرشيف= https://web.archive.org/web/20200304173120/https://books.google.com/?id=aFDWuZZslUUC&pg=PA1211&lpg=PA1211&dq=Golomb%E2%80%93Dickman+constant#v=onepage&q=Golomb%E2%80%93Dickman%20constant&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>{\lambda}</math>
||<math>\int \limits_0^\infty \underset{\text{Para } x>2}{\frac{f(x)}{x^2} \, dx} = \int \limits_0^1 e^{\operatorname{Li}(n)} dn \quad \scriptstyle \text{Li: Logarithmic integral}</math>
||<syntaxhighlight lang="mathematica">N[Int{n,0,1}[e^Li(n)],34]</syntaxhighlight>
||
||{{OEIS2C|A084945}}
||[0;1,1,1,1,1,22,1,2,3,1,1,11,1,1,2,22,2,6,1,...]
||1930 <br /> & <br /> 1964
||<small> 0.62432998854355087099293638310083724 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|23.1406926327792690057
||[[ثابتة غيلفوند|ثابت غيلفوند]] <ref>{{استشهاد بكتاب 
|مؤلف= David Wells
|عنوان= The Penguin Dictionary of Curious and Interesting Numbers
|مسار= https://books.google.com/?id=7L7xcjBPemEC&pg=RA2-PA4&dq=23.14069#v=onepage&q=23.14069&f=false
|سنة= 1997
|ناشر= Penguin Books Ltd.
|isbn= 
|صفحة= 4
|مسار أرشيف= https://web.archive.org/web/20200304173122/https://books.google.com/?id=7L7xcjBPemEC&pg=RA2-PA4&dq=23.14069#v=onepage&q=23.14069&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>{e}^{\pi}</math>
||<math> (-1)^{-i} = i^{-2i} = \sum_{n=0}^\infty \frac{\pi^{n}}{n!} = \frac{\pi^{1}}{1} + \frac{\pi^{2}}{2!} + \frac{\pi^{3}}{3!} + \cdots</math>
||<syntaxhighlight lang="mathematica">Sum[n=0 to ∞] 
 {(pi^n)/n!}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A039661}}
||[23;7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,...]
||
||<small> 23.1406926327792690057290863679485474 </small>
<!-- 0.04321391826377224977441773717172801<br> ''1/C = (-1)^i = e^-pi'' = {{OEIS2C|A093580}} -->
|-

<!---------------------------------------------v---------------------------------------->
|7.38905609893065022723
||[[ثابت مخروطي|الثابت المخروطى]]، [[ثابت مخروطي|ثابت شوارتزشيلد]] <ref>{{استشهاد بكتاب 
|مؤلف1=Jvrg Arndt |مؤلف2=Christoph Haenel |عنوان= Pi: Algorithmen, Computer, Arithmetik
|مسار= https://books.google.com/?id=mchJCvIsSXwC&pg=PA67&dq=7.38905#v=onepage&q=7.38905&f=false
|ناشر= Springer
|isbn= 3-540-66258-8
|صفحة= 67
|مسار أرشيف= https://web.archive.org/web/20200304173124/https://books.google.com/?id=mchJCvIsSXwC&pg=PA67&dq=7.38905#v=onepage&q=7.38905&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Conic constant.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>e^2</math>
||<math> \sum_{n = 0}^\infty \frac{2^n}{n!} = 1+2+\frac{2^2}{2!}+\frac{2^3}{3!}+\frac{2^4}{4!}+\frac{2^5}{5!}+\cdots</math>
|| <syntaxhighlight lang="mathematica">Sum[n=0 to ∞]
{2^n/n!}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A072334}}
||[7;2,1,1,3,18,5,1,1,6,30,8,1,1,9,42,11,1,...]<br />= [7,2,{{سطر فوقي|1,1,n,4*n+6,n+2}}], n = 3, 6, 9, etc.
||
||<small> 7.38905609893065022723042746057500781 </small> 
|-

<!------------------------------------------v------------------------------------------->
|0.35323637185499598454
||ثابت هافنر – سارنك – مككورليي (1) <ref>{{استشهاد بكتاب 
|مؤلف= Steven R. Finch
|عنوان= Mathematical Constants
|مسار= https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA110&dq=%22Hafner-Sarnak-McCurley+constant%22#v=onepage&q=%22Hafner-Sarnak-McCurley%20constant%22&f=false
|سنة= 2003
|ناشر= 
|isbn= 3-540-67695-3
|صفحة= 110
|مسار أرشيف= https://web.archive.org/web/20200304173126/https://books.google.com/?id=Pl5I2ZSI6uAC&pg=PA110&dq=%22Hafner-Sarnak-McCurley+constant%22#v=onepage&q=%22Hafner-Sarnak-McCurley%20constant%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\sigma}</math>
||<math> \prod_{k=1}^{\infty}\left\{1-[1-\prod_{j=1}^n \underset{p_k: \text{ prime}}{(1-p_k^{-j})]^2}\right\}</math>
||<syntaxhighlight lang="mathematica">prod[k=1 to ∞] 
{1-(1-prod[j=1 to n] 
{1-ithprime(k)^-j})^2}</syntaxhighlight> 
||
||{{OEIS2C|A085849}}
||[0;2,1,4,1,10,1,8,1,4,1,2,1,2,1,2,6,1,1,1,3,...]
||1993
||<small> 0.35323637185499598454351655043268201 </small> 
|-

<!------------------------------------------v------------------------------------------->
|0.60792710185402662866
||ثابت هافنر – سارنك – مككورليي (2) <ref>{{استشهاد بكتاب 
|مؤلف1=Holger Hermanns |مؤلف2=Roberto Segala |عنوان= Process Algebra and Probabilistic Methods.
|مسار= https://books.google.com/?id=007-3SM9QmYC&pg=PA270&dq=0.607927101854026628663276779#v=onepage&q=0.607927101854026628663276779&f=false
|سنة= 2000
|ناشر= Springer-Verlag
|isbn= 3-540-67695-3
|صفحة= 270
|مسار أرشيف= https://web.archive.org/web/20200304173128/https://books.google.com/?id=007-3SM9QmYC&pg=PA270&dq=0.607927101854026628663276779#v=onepage&q=0.607927101854026628663276779&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>\frac{1}{\zeta(2)}</math>
||<math> \frac{6}{\pi^2} = \prod_{n = 0}^\infty \underset{p_n: \text{ prime}}{\! \left(\! 1- \frac{1}{{p_n}^2} \! \right)} \! = \! \textstyle \left(1 \! - \! \frac{1}{2^2}\right) \! \left(1 \! - \! \frac{1}{3^2}\right) \! \left(1 \! - \! \frac{1}{5^2}\right)\cdots</math>
||<syntaxhighlight lang="mathematica">Prod{n=1 to ∞}
(1-1/ithprime(n)^2)</syntaxhighlight> 
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A059956}}
||[0;1,1,1,1,4,2,4,7,1,4,2,3,4,10,1,2,1,1,1,...] 
||
||<small> 0.60792710185402662866327677925836583 </small> 
|-

<!------------------------------------------v------------------------------------------->
| 0.12345678910111213141
||ثابت تشامبيرنوون <ref>{{استشهاد بكتاب 
|مؤلف1=Michael J. Dinneen |مؤلف2=Bakhadyr Khoussainov |مؤلف3=Prof. Andre Nies |عنوان= Computation, Physics and Beyond
|مسار= https://books.google.com/?id=wRWyMbmJTMYC&pg=PA109&dq=%22Champernowne+number%22#v=onepage&q=%22Champernowne%20number%22&f=false
|سنة= 2012 
|ناشر= Springer
|isbn= 978-3-642-27653-8
|صفحة= 110 
|مسار أرشيف= https://web.archive.org/web/20200304173130/https://books.google.com/?id=wRWyMbmJTMYC&pg=PA109&dq=%22Champernowne+number%22#v=onepage&q=%22Champernowne%20number%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Champernowne constant.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>C_{10}</math>
||<math>\sum_{n=1}^\infty \; \sum_{k=10^{n-1}}^{10^n-1}\frac{k}{10^{kn-9\sum_{j=0}^{n-1}10^j(n-j-1)}}</math>
||
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A033307}}
||[0;8,9,1,149083,1,1,1,4,1,1,1,3,4,1,1,1,15,...]
||1933
||<small> 0.12345678910111213141516171819202123 </small> 
|-

<!-----------------------------------------v-------------------------------------------->
| 0.76422365358922066299
||ثابت [[سرينفاسا أينجار رامانجن|رامانجن]]-[[إدموند لاندو|لاندو]] <ref>{{استشهاد بكتاب 
|مؤلف1=Richard E. Crandall |مؤلف2=Carl B. Pomerance |عنوان= Prime Numbers: A Computational Perspective
|مسار= https://books.google.com/?id=ZXjHKPS1LEAC&pg=PA80&dq=Landau-Ramanujan+constant#v=onepage&q=Landau-Ramanujan%20constant&f=false 
|سنة= 2005  
|ناشر= Springer
|isbn= 978-0387-25282-7
|صفحة= 80
|مسار أرشيف= https://web.archive.org/web/20200304173133/https://books.google.com/books?id=ZXjHKPS1LEAC&pg=PA80&dq=Landau-Ramanujan+constant&hl=en#v=onepage&q=Landau-Ramanujan%20constant&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>K</math>
||<math>\frac1{\sqrt2}\prod_{p\equiv3\!\!\!\!\!\mod \! 4}\!\! \underset{\!\!\!\!\!\!\!\! p: \text{ prime}}{\left(1-\frac1{p^2}\right)^{-\frac{1}{2}}}\!\!=\frac\pi4\prod_{p\equiv1\!\!\!\!\!\mod \!4}\!\! \underset{\!\!\!\! p: \text{ prime}}{\left(1-\frac1{p^2}\right)^\frac{1}{2}}</math>
||
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A064533}}
||[0;1,3,4,6,1,15,1,2,2,3,1,23,3,1,1,3,1,1,6,4,...]
||
||<small> 0.76422365358922066299069873125009232 </small> 
|-

<!------------------------------------------v------------------------------------------->
|2.71828182845904523536
||العدد [[ه (رياضيات)|ه]]، [[ه (رياضيات)|العدد النيبيري]]، [[أعداد أويلر|عدد أويلر]] <ref>{{استشهاد بكتاب
|مؤلف= E.Kasner y J.Newman.
|عنوان= Mathematics and the Imagination
|صفحة=77
|سنة= 2007
|ناشر= Conaculta
|isbn= 978-968-5374-20-0
|مسار= https://books.google.com/?id=zdBHMHV3m5YC&pg=PA76&dq=2.7182818284590452353602874#v=onepage&q=2.7182818284590452353602874&f=false
|مسار أرشيف= https://web.archive.org/web/20200304173135/https://books.google.com/books?id=zdBHMHV3m5YC&pg=PA76&dq=2.7182818284590452353602874&hl=en#v=onepage&q=2.7182818284590452353602874&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Exp derivative at 0.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{e}</math>
||<math>\! \lim_{n \to \infty} \! \left( \! 1 \! + \! \frac {1}{n}\right)^n \! = \! \sum_{n = 0}^\infty \frac{1}{n!} = \frac{1}{0!} + \frac{1}{1} + \frac{1}{2!} + \frac{1}{3!} + \textstyle \cdots </math>
||<syntaxhighlight lang="mathematica">Sum[n=0 to ∞]
{1/n!} 
(* lim_(n->∞) 
(1+1/n)^n *)</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A001113}}
||[2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,...] <br /> = [2;{{سطر فوقي|1,2p,1}}], p∈ℕ
||
||<small> 2.71828182845904523536028747135266250 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|0.3678794411714423215955
||معكوس [[ه (رياضيات)|العدد ه]]، معكوس [[ه (رياضيات)|العدد النيبيري]]، معكوس [[أعداد أويلر|عدد أويلر]] <ref>{{استشهاد بكتاب 
|مؤلف= Eli Maor 
|عنوان= "e": The Story of a Number
|مسار= https://books.google.com/?id=eIsyLD_bDKkC&pg=PA37&dq=0.367879441#v=onepage&q=0.367879441&f=false
|سنة= 1994 
|ناشر= Princeton University Press
|isbn= 978-0-691-14134-3
|صفحة= 37
|مسار أرشيف= https://web.archive.org/web/20200304173137/https://books.google.com/?id=eIsyLD_bDKkC&pg=PA37&dq=0.367879441#v=onepage&q=0.367879441&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>\frac{1}{e}</math>
||<math>\sum_{n = 0}^\infty \frac{(-1)^n}{n!} = \frac{1}{0!} - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \frac{1}{5!} +\cdots</math>
<!--- 2\cdot(1/3! +2/5! +3/7!+\cdots --->
||<syntaxhighlight lang="mathematica">Sum[n=2 to ∞]
{(-1)^n/n!}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A068985}}
||[0;2,1,1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,...] <br /> = [0;2,1,{{سطر فوقي|1,2p,1}}], p∈ℕ
||1618
||<small> 0.36787944117144232159552377016146086 </small> 
|-

<!----------------------------------------------v--------------------------------------->
|0.69034712611496431946
||[[نهاية (رياضيات)|الحد الأعلى]] [[دالة أسية|للدالة الأسية]] المكررة<ref>{{استشهاد بكتاب 
|مؤلف= Theo Kempermann
|عنوان= Zahlentheoretische Kostproben
|مسار= https://books.google.com/?id=c70frvZ9TEQC&pg=PA139&lpg=PA139&dq=0.690347+0.658366#v=onepage&q=0%2C690347%200%2C658366&f=false
|سنة= 2005
|ناشر= Freiburger graphische betriebe
|isbn= 3-8171-1780-9
|صفحة= 139
|مسار أرشيف= https://web.archive.org/web/20200414182754/https://books.google.com/?id=c70frvZ9TEQC&pg=PA139&lpg=PA139&dq=0.690347+0.658366#v=onepage&q=0%2C690347%200%2C658366&f=false|تاريخ أرشيف=2020-04-14}}</ref>
||[[ملف:TetrationConvergence2D.png|100px]]
|bgcolor=#e0f0f0 align=center|<math> {H}_{2n+1} </math>
||<math> \lim_{n \to \infty} {H}_{2n+1} = 
\textstyle \left(\frac{1}{2}\right)
^{\left(\frac{1}{3}\right)
^{\left(\frac{1}{4}\right)
^{\cdot^{\cdot^{\left(\frac{1}{2n+1}\right)}}}}}
 = {2}^{-3^{-4^{\cdot^{\cdot^{{-2n-1}}}}}} </math> 
||<syntaxhighlight lang="mathematica">2^-3^-4^-5^-6^ 
 -7^-8^-9^-10^ 
 -11^-12^-13 …</syntaxhighlight>
||
||{{OEIS2C|A242760}}
||[0;1,2,4,2,1,3,1,2,2,1,4,1,2,4,3,1,1,10,1,3,2,...]
||
||<small> 0.69034712611496431946732843846418942 </small>
|-

<!--------------------------------------------v----------------------------------------->
|0.6583655992 
||[[نهاية (رياضيات)|الحد الأدنى]] [[دالة أسية|للدالة الأسية]] المكررة <ref>{{استشهاد بكتاب 
|مؤلف= Steven Finch
|عنوان= Mathematical Constants
|مسار= https://books.google.com/?id=DL5iVYNoEa0C&pg=PA449&lpg=PA449&dq=0.6583655992#v=onepage&q=0.6583655992&f=false
|سنة= 2003 
|ناشر= Cambridge University Press 
|isbn= 0-521-81805-2
|صفحة= 449
|مسار أرشيف= https://web.archive.org/web/20200304173140/https://books.google.com/?id=DL5iVYNoEa0C&pg=PA449&lpg=PA449&dq=0.6583655992#v=onepage&q=0.6583655992&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
 |bgcolor=#e0f0f0 align=center|<math> {H}_{2n} </math>
||<math> \lim_{n \to \infty} {H}_{2n} = 
\textstyle \left(\frac{1}{2}\right)
^{\left(\frac{1}{3}\right)
^{\left(\frac{1}{4}\right)
^{\cdot^{\cdot^{\left(\frac{1}{2n}\right)}}}}}
 = {2}^{-3^{-4^{\cdot^{\cdot^{{-2n}}}}}} </math> 
||<syntaxhighlight lang="mathematica">2^-3^-4^-5^-6^ 
 -7^-8^-9^-10^ 
 -11^-12 …</syntaxhighlight>
||
||
||[0;1,1,1,12,1,2,1,1,4,3,1,1,2,1,2,1,51,2,2,1,...]
||
||0.6583655992. 
|-

<!------------------------------------------v------------------------------------------->
|3.14159265358979323846264
||[[ط (رياضيات)|ط]]، [[ط (رياضيات)|ثابت أرخميدس]]، [[ط (رياضيات)|ثابت الدائرة]]، [[ط (رياضيات)|باي]] <ref>{{استشهاد بكتاب 
|مؤلف= Michael Trott
|عنوان= The Mathematica GuideBook for Programming
|مسار= https://books.google.com/?id=iZTxaxT_YeMC&pg=PA173&dq=pi+nested+radical#v=onepage&q=pi%20nested%20radical&f=false 
|سنة= 2004
|ناشر= Springer Science
|isbn= 0-387-94282-3
|صفحة= 173
|مسار أرشيف= https://web.archive.org/web/20200304173142/https://books.google.com/?id=iZTxaxT_YeMC&pg=PA173&dq=pi+nested+radical#v=onepage&q=pi%20nested%20radical&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Sine cosine one period.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math> \pi </math>
||<math>\lim_{n\to \infty }\, 2^n \underbrace{\sqrt{2-\sqrt{2+\sqrt{2+\cdots +\sqrt{2}}}}}_n</math>
||<syntaxhighlight lang="mathematica">Sum[n=0 to ∞]
{(-1)^n 4/(2n+1)}</syntaxhighlight> 
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A000796}}
||[3;7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,...]
||
||<small> 3.14159265358979323846264338327950288 </small> 
|-

<!---------------------------------------------v---------------------------------------->
|1.9287800 
||ثابت رايت <ref>{{استشهاد بكتاب 
|مؤلف= Paulo Ribenboim 
|عنوان= My Numbers, My Friends: Popular Lectures on Number Theory
|مسار= https://books.google.com/?id=EiYvlcimEi4C&pg=PA66&dq=1.9287800#v=onepage&q=1.9287800&f=false
|سنة= 2000 
|ناشر= Springer-Verlag
|isbn= 0-387-98911-0
|صفحة= 66 
|مسار أرشيف= https://web.archive.org/web/20200304172858/https://books.google.com/?id=EiYvlcimEi4C&pg=PA66&dq=1.9287800#v=onepage&q=1.9287800&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>{\omega}</math>
||<math>\left \lfloor 2^{2^{2^{\cdot^{\cdot^{2^{\omega}}}}}} \!\right \rfloor \scriptstyle \text{= primes:} \displaystyle\left\lfloor 2^\omega\right\rfloor \scriptstyle \text{=3,} 
\displaystyle\left\lfloor 2^{2^\omega} \right\rfloor \scriptstyle \text{=13,} 
\displaystyle \left\lfloor 2^{2^{2^\omega}} \right\rfloor \scriptstyle =16381, \ldots </math>
||
||
||{{OEIS2C|A086238}}
||[1; 1, 13, 24, 2, 1, 1, 3, 1, 1, 3]
||
||1.9287800
|-

<!-----------------------------------------v-------------------------------------------->
| 0.4636476090008061162142
||سلسلة ماشين-غريغوري<ref>{{استشهاد بكتاب 
|مؤلف1=John Horton Conway |مؤلف2=Richard K. Guy. |عنوان= The Book of Numbers
|مسار= https://books.google.com/?id=0--3rcO7dMYC&pg=PA242&dq=%22The+Book+of+Numbers%22+%22mathematician+David+Gregory%22#v=onepage&q=%22The%20Book%20of%20Numbers%22%20%22mathematician%20David%20Gregory%22&f=false
|سنة= 1995
|ناشر= Copernicus
|isbn= 0-387-97993-X
|صفحة= 242
|اقتباس=
|مسار أرشيف= https://web.archive.org/web/20200304173145/https://books.google.com/?id=0--3rcO7dMYC&pg=PA242&dq=%22The+Book+of+Numbers%22+%22mathematician+David+Gregory%22#v=onepage&q=%22The%20Book%20of%20Numbers%22%20%22mathematician%20David%20Gregory%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Arctangent.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>\arctan \frac {1}{2}</math>
||<math>  \underset{\text{For } x = 1/2 \qquad \qquad} {\sum_{n=0}^\infty \frac{(\!-1\!)^n \, x^{2n+1}}{2n+1} = \frac {1}{2} {-} \frac{1}{3 \! \cdot \! 2^3} {+} \frac{1}{5 \! \cdot \! 2^5} {-} \frac{1}{7 \! \cdot \! 2^7} {+} \cdots}</math>
||<syntaxhighlight lang="mathematica">Sum[n=0 to ∞] 
{(-1)^n (1/2)^(2n+1)
/(2n+1)}</syntaxhighlight>
|'''[[عدد غير كسري|غ.ك]]'''
||{{OEIS2C|A073000}}
||[0;2,6,2,1,1,1,6,1,2,1,1,2,10,1,2,1,2,1,1,1,...]
||
||<small> 0.46364760900080611621425623146121440 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|0.6977746579640079820067
||ثابت [[كسر مستمر|الكسر المستمر]]، [[دالة بيسل]]<ref>{{استشهاد بكتاب
|مؤلف= Simon Plouffe
|عنوان= Miscellaneous Mathematical Constants
|مسار= http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap69.html
| مسار أرشيف = https://web.archive.org/web/20150912180856/http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap69.html | تاريخ أرشيف = 12 سبتمبر 2015 }}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{C}_{CF}</math>
||<math> \frac{I_1(2)}{I_0(2)} = \frac{ \sum \limits_{n = 0}^\infty \frac{n}{n!n!}} {{ \sum \limits_{n = 0}^{\infty} \frac{1}{n!n!}}} =
 \textstyle \tfrac 1{1+\tfrac 1{2+\tfrac 1{3+\tfrac 1{4+\tfrac 1{5+\tfrac 1{6+1{/\cdots}}}}}}} </math>
<!--- 1/(1+1/(1+1/(1+2/(1+2/(1+3/(1+3/(1+4))))))) demo Wolfram --->
||<syntaxhighlight lang="mathematica">(Sum [n=0 to ∞]
{n/(n!n!)}) /
(Sum [n=0 to ∞]
{1/(n!n!)})</syntaxhighlight>
|'''[[عدد غير كسري|غ.ك]]'''
||{{OEIS2C|A052119}}
||[0;1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,...] <br /> = [0;{{سطر فوقي|p+1}}], p∈ℕ
<!--- 1/(1+1/(2+1/(3+1/(4+1/(5+1/(6+1/(7+1/(8+1))))))))--->
||
||<small> 0.69777465796400798200679059255175260 </small> 
|-

<!--------------------------------------------v----------------------------------------->
|1.902160583104 
||<small>[[مبرهنة برون]] = Σ مجموع [[مقلوب (توضيح)|مقلوب]] [[عددان أوليان توأم|الأعداد الأولية التوأم]]</small> <ref>{{استشهاد بكتاب 
|مؤلف= Thomas Koshy
|عنوان= Elementary Number Theory with Applications
|مسار= https://books.google.com/?id=d5Z5I3gnFh0C&pg=PA118&dq=Brun+constant#v=onepage&q=Brun%20constant&f=false
|سنة= 2007
|ناشر= Elsevier
|isbn= 978-0-12-372-487-8
|صفحة= 119
|مسار أرشيف= https://web.archive.org/web/20200304173147/https://books.google.com/?id=d5Z5I3gnFh0C&pg=PA118&dq=Brun+constant#v=onepage&q=Brun%20constant&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Bruns-constant.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{B}_{\,2}</math>
||<math> \textstyle \underset{ p,\, p+2: \text{ prime}}{\sum(\frac1{p}+\frac1{p+2})} = (\frac1{3} \! + \! \frac1{5}) + (\tfrac1{5} \! + \! \tfrac1{7}) + (\tfrac1{11} \! + \! \tfrac1{13}) + \cdots </math>
||
||
||{{OEIS2C|A065421}}
||[1; 1, 9, 4, 1, 1, 8, 3, 4, 4, 2, 2]
||
||1.902160583104 
|-

<!-------------------------------------------v------------------------------------------>
|0.870588379975 
||<small>[[مبرهنة برون]] = Σ مجموع مقلوب مجموعة التوأم الرباعي</small> <ref>{{استشهاد بكتاب 
|مؤلف1=Pascal Sebah  |مؤلف2=Xavier Gourdon
 |lastauthoramp=yes |عنوان= Introduction to twin primes and Brun’s constant computation
|مسار= http://numbers.computation.free.fr/Constants/Primes/twin.pdf
|سنة= 2002
|ناشر= 
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20161022135640/http://numbers.computation.free.fr/Constants/Primes/twin.pdf | تاريخ أرشيف = 22 أكتوبر 2016 }}</ref>
||<br /><br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math>{B}_{\,4}</math>
||<math>\textstyle {\sum(\frac1{p}+\frac1{p+2}+\frac1{p+6}+\frac1{p+8})} \scriptstyle \quad {p,\; p+2,\; p+6,\; p+8: \text{ prime}} </math>
<math> \textstyle{\left(\tfrac1{5} + \tfrac1{7} + \tfrac1{11} + \tfrac1{13}\right)}+ \left(\tfrac1{11} + \tfrac1{13} + \tfrac1{17} + \tfrac1{19}\right)+ \dots</math>
||
||
||{{OEIS2C|A213007}}
||[0; 1, 6, 1, 2, 1, 2, 956, 3, 1, 1]
||
||0.870588379975 
|-

<!------------------------------------------v------------------------------------------->
|<br />
0.63661977236758134307
||ثابت بوفون<ref>{{استشهاد بكتاب
|مؤلف1=Jorg Arndt |مؤلف2=Christoph Haenel |عنوان= Pi -- Unleashed
|صفحة= 13
|سنة= 2000
|ناشر= Verlag Berlin Heidelberg
|isbn= 3-540-66572-2
|مسار= https://books.google.com/?id=QwwcmweJCDQC&pg=PA13&dq=Fran%C3%A7ois+Vi%C3%A8te+(1540-1603)+developed#v=onepage&q=Fran%C3%A7ois%20Vi%C3%A8te%20(1540-1603)%20developed&f=false
|مسار أرشيف= https://web.archive.org/web/20200304173149/https://books.google.com/?id=QwwcmweJCDQC&pg=PA13&dq=Fran%C3%A7ois+Vi%C3%A8te+(1540-1603)+developed#v=onepage&q=Fran%C3%A7ois%20Vi%C3%A8te%20(1540-1603)%20developed&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Buffon2.png|100px]]
|bgcolor=#e0f0f0 align=center|<math>\frac{2}{\pi}</math>
||<math> \frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdots</math> <br />
[[صيغة فييت]]
||<syntaxhighlight lang="mathematica">2/Pi</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A060294}}
||[0;1,1,1,3,31,1,145,1,4,2,8,1,6,1,2,3,1,4,...]
||1540 <br /> to <br /> 1603
||<small> 0.63661977236758134307553505349005745 </small> 
|-

<!--------------------------------------------v----------------------------------------->
| 0.59634736232319407434
||ثابت جومبرتز <ref>{{استشهاد بكتاب 
|مؤلف1=Annie Cuyt |مؤلف2=Viadis Brevik Petersen |مؤلف3=Brigitte Verdonk |مؤلف4=William B. Jones |عنوان= Handbook of continued fractions for special functions
|مسار= https://books.google.com/?id=DQtpJaEs4NIC&pg=PA190&dq=Gompertz+constant#v=onepage&q=Gompertz%20constant&f=false
|سنة= 2008
|ناشر= Springer Science 
|isbn= 978-1-4020-6948-2
|صفحة= 190
|مسار أرشيف= https://web.archive.org/web/20200304173152/https://books.google.com/?id=DQtpJaEs4NIC&pg=PA190&dq=Gompertz+constant#v=onepage&q=Gompertz%20constant&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{G}</math>
||<math>\! \int \limits_0^\infty \!\! \frac{e^{-n}}{1{+}n} \, dn = \!\! \int \limits_0^1 \!\! \frac{1}{1{-}\ln n} \, dn =
 \textstyle {\tfrac 1 {1+\tfrac 1{1+\tfrac 1{1+\tfrac 2{1+\tfrac 2{1+\tfrac 3{1+3{/\cdots}} }}}}}} </math>
<!--- 1/(1+1/(1+1/(1+2/(1+2/(1+3/(1+3))))))) demo Wolfram --->
||<syntaxhighlight lang="mathematica">integral[0 to ∞]
{(e^-n)/(1+n)}</syntaxhighlight>
|'''[[عدد غير كسري|غ.ك]]'''
||{{OEIS2C|A073003}}
||[0;1,1,2,10,1,1,4,2,2,13,2,4,1,32,4,8,1,1,1,...]
<!--- 1/(1+1/(1+1/(2+1/(10+1/(1+1/(1+1/(4+1))))))) demo Wolfram --->
||
||<small> 0.59634736232319407434107849936927937 </small> 
|-

<!----------------------------------------v--------------------------------------------->
|<div style="text-align: center;"> '''''ت''''' </div>
||[[وحدة تخيلية]] <ref>{{استشهاد بكتاب 
|مؤلف= Keith J. Devlin 
|عنوان= Mathematics: The New Golden Age
|مسار= https://books.google.com/?id=IKmMKOtSI50C&pg=PA66&dq=%22This+leads+to+some+amazing+results.+For+example,+Euler+discovered%22#v=onepage&q=%22This%20leads%20to%20some%20amazing%20results.%20For%20example%2C%20Euler%20discovered%22&f=false
|سنة= 1999
|ناشر= Columbia University Press
|isbn= 0-231-11638-1
|صفحة= 66
|مسار أرشيف= https://web.archive.org/web/20200614201959/https://books.google.com/books?id=IKmMKOtSI50C&pg=PA66&dq=%22This+leads+to+some+amazing+results.+For+example,+Euler+discovered%22&hl=en#v=onepage&q=%22This%20leads%20to%20some%20amazing%20results.%20For%20example,%20Euler%20discovered%22&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Complex numbers imaginary unit.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{i}</math>
||<math>\sqrt{-1} = \frac{\ln(-1)}{\pi} \qquad\qquad \mathrm{e}^{i\,\pi} = -1</math>
||<syntaxhighlight lang="mathematica">sqrt(-1)</syntaxhighlight>
|'''[[عدد غير كسري|غ.ك]]'''، '''[[عدد مركب|خ]]'''
|| 
||
||1501 <br/> to <br/> 1576
||<div style="text-align: center;"> '''''i''''' </div>
|-

<!---------------------------------------------v---------------------------------------->
|2.74723 82749 32304 33305
||ثابت [[سرينفاسا أينجار رامانجن|رامانجن]] للمتداخلة الجذرية <ref>{{استشهاد بكتاب 
|مؤلف1=Bruce C. Berndt |مؤلف2=Robert Alexander Rankin |عنوان= Ramanujan: essays and surveys
|مسار= https://books.google.com/?id=TT1T8A94xNcC&pg=PA219&dq=Ramanujan+nested+radical#v=onepage&q=Ramanujan%20nested%20radical&f=false
|سنة= 2001 
|ناشر= American Mathematical Society, London Mathematical Society
|isbn= 0-8218-2624-7
|صفحة= 219
|مسار أرشيف= https://web.archive.org/web/20200304173156/https://books.google.com/?id=TT1T8A94xNcC&pg=PA219&dq=Ramanujan+nested+radical#v=onepage&q=Ramanujan%20nested%20radical&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||<br /><br /><br /><br />
|bgcolor=#e0f0f0 align=center|<math> R_{5} </math>
||<math>\scriptstyle \sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+
                     \sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}}\;=
        \textstyle\frac{2+\sqrt{5}+\sqrt{15-6\sqrt{5}}}{2}</math>
||<syntaxhighlight lang="mathematica">(2+sqrt(5)
+sqrt(15
-6 sqrt(5)))/2</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||
||[2;1,2,1,21,1,7,2,1,1,2,1,2,1,17,4,4,1,1,4,2,...]
||
||<small> 2.74723827493230433305746518613420282 </small> 
|-

<!------------------------------------------v------------------------------------------->
|0.56714 32904 09783 87299 
||ثابت أوميجا <ref>{{استشهاد بكتاب 
|مؤلف= Albert Gural 
|عنوان= Infinite Power Towers
|مسار= http://www.albertgural.com/math/theory/infinite-power-towers/
| مسار أرشيف = https://web.archive.org/web/20190421000309/http://www.albertgural.com/math/theory/infinite-power-towers/ | تاريخ أرشيف = 21 أبريل 2019 }}</ref>
||[[ملف:Lambert-w.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math>{\Omega}</math>
||<math> \sum_{n=1}^\infty \frac{(-n)^{n-1}}{n!} 
 =\,\left(\frac{1}{e}\right)
^{\left(\frac{1}{e}\right)
^{\cdot^{\cdot^{\left(\frac{1}{e}\right)}}}}
= e^{-\Omega} = e^{-e^{-e^{\cdot^{\cdot^{{-e}}}}}} </math> 
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞]
{(-n)^(n-1)/n!}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A030178}}
||[0;1,1,3,4,2,10,4,1,1,1,1,2,7,306,1,5,1,2,1,...]
||
||<small> 0.56714329040978387299996866221035555 </small> 
|-

<!-------------------------------------------v------------------------------------------>
|0.968946146259369380483
||[[بيتا (توضيح)|بيتا]](3) <ref>{{استشهاد بأرخايف 
|author= Michael A. Idowu
|title= Fundamental relations between the Dirichlet beta function, euler numbers, and Riemann zeta function for positive integers
|arxiv= 1210.5559
|year= 2012
|class=math.NT
}}</ref>
||
|bgcolor=#e0f0f0 align=center|<math>{\beta} (3)</math>
|| <math> \frac{\pi^3}{32} = \sum_{n=1}^\infty\frac{-1^{n+1}}{(-1+2n)^3} = \frac{1}{1^3} {-} \frac{1}{3^3} {+} \frac{1}{5^3} {-} \frac{1}{7^3} {+} \cdots </math>
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞]
{(-1)^(n+1)
/(-1+2n)^3}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A153071}}
||[0;1,31,4,1,18,21,1,1,2,1,2,1,3,6,3,28,1,...]
||
||<small> 0.96894614625936938048363484584691860 </small> 
|-

<!------------------------------------------v------------------------------------------->
|2.236067977499789696409
||[[الجذر التربيعي ل 5]]، [[مجموع غاوس]] <ref>{{استشهاد بكتاب 
|مؤلف= P A J Lewis  
|عنوان= Essential Mathematics 9
|مسار= https://books.google.com/?id=KjMVx6ljh6YC&pg=PA24&dq=2.236067977#v=onepage&q=2.236067977&f=false
|سنة= 2008
|ناشر= Ratna Sagar
|isbn= 9788183323673
|صفحة= 24
|اقتباس=
|مسار أرشيف= https://web.archive.org/web/20200304173158/https://books.google.com/?id=KjMVx6ljh6YC&pg=PA24&dq=2.236067977#v=onepage&q=2.236067977&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:Pinwheel 1.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math> \sqrt{5} </math>
||<math> \scriptstyle  (n = 5) \displaystyle  \sum_{k=0}^{n-1} e^{\frac{2 k^2 \pi i}{n}} = 1 + e^\frac{2 \pi i} {5} + e^\frac{8 \pi i} {5} + e^\frac{18 \pi i} {5} + e^\frac{32 \pi i} {5}</math>
||<syntaxhighlight lang="mathematica">Sum[k=0 to 4]
{e^(2k^2 pi i/5)}</syntaxhighlight>
|'''[[عدد جبري|ج]]'''
||{{OEIS2C|A002163}}
||[2;4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,...] <br /> = [2;{{سطر فوقي|4}},...]
||
||<small> 2.23606797749978969640917366873127624 </small> 
|-

<!--------------------------------------------v----------------------------------------->
| 3.35988566624317755317
||ثابت [[ليوناردو فيبوناتشي|فيبوناتشي]]<ref>{{استشهاد بكتاب 
|مؤلف= Gérard P. Michon
|عنوان= Numerical Constants
|مسار= http://www.numericana.com/answer/constants.htm#prevost
|سنة= 2005
|ناشر= Numericana
|isbn= 
| مسار أرشيف = https://web.archive.org/web/20190119141655/http://www.numericana.com/answer/constants.htm | تاريخ أرشيف = 19 يناير 2019 }}</ref>
||
|bgcolor=#e0f0f0 align=center|<math> \Psi </math>
||<math>\sum_{n=1}^{\infty} \frac{1}{F_n} = \frac{1}{1} +  \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{8} + \frac{1}{13} + \cdots</math>
''F<sub>n</sub>'': [[عدد فيبوناتشي|متتالية فيبوناتشي]]
||<syntaxhighlight lang="mathematica">Sum[n=1 to ∞]
{1/Fibonacci[n]}</syntaxhighlight>
|'''[[عدد غير كسري|غ.ك]]'''
||{{OEIS2C|A079586}}
||[3;2,1,3,1,1,13,2,3,3,2,1,1,6,3,2,4,362,...]
||
||<small> 3.35988566624317755317201130291892717 </small> 
|-

<!------------------------------------------v------------------------------------------->
|2.685452001065306445309
||ثابت خينتشين <ref>{{استشهاد بكتاب 
|مؤلف= Julian Havil
|عنوان= Gamma: Exploring Euler's Constant
|مسار= https://books.google.com/?id=7-sDtIy8MNIC&pg=PA161&dq=Khinchin%27s+constant#v=onepage&q=Khinchin%27s%20constant&f=false
|سنة= 2003 
|ناشر= Princeton University Press
|isbn= 9780691141336 
|صفحة= 161
|مسار أرشيف= https://web.archive.org/web/20200304173016/https://books.google.com/?id=7-sDtIy8MNIC&pg=PA161&dq=Khinchin%27s+constant#v=onepage&q=Khinchin%27s%20constant&f=false|تاريخ أرشيف=2020-03-04}}</ref>
||[[ملف:KhinchinBeispiele.svg|100px]]
|bgcolor=#e0f0f0 align=center|<math> K_{\,0} </math>
||<math> \prod_{n=1}^\infty \left[{1+{1\over n(n+2)}}\right]^{\ln n/\ln 2}</math>
||<syntaxhighlight lang="mathematica">Prod[n=1 to ∞] 
 {(1+1/(n(n+2))) 
 ^(ln(n)/ln(2))}</syntaxhighlight>
|'''[[عدد متسام|م]]'''
||{{OEIS2C|A002210}}
||[2;1,2,5,1,1,2,1,1,3,10,2,1,3,2,24,1,3,2,...]
||1934
||<small> 2.68545200106530644530971483548179569 </small> 
|-

<!-------------------------------------------.------------------------------------------>
|}

== انظر أيضًا ==
* [[قائمة الرموز الرياضية حسب الموضوع|قائمة الرموز الرياضية بحسب الموضوع]]
* [[قائمة الرموز الرياضية بحسب التاريخ]]
* [[قائمة الأعداد]]
* [[ثابت رياضي]]
* [[لامتغير (رياضيات)|لامتغير]]

== المصادر ==
<div style="height:10em; overflow:auto; border: 2px solid #088">
{{مراجع|30em}}
</div>
{{شريط بوابات|نظرية الأعداد|رياضيات}}

[[تصنيف:أعداد جبرية]]
[[تصنيف:ثوابت رياضية]]
[[تصنيف:جداول رياضيات]]
[[تصنيف:قوائم متعلقة بالرياضيات]]
[[تصنيف:قوائم مرتبطة بالأعداد]]
[[تصنيف:كسور مستمرة]]