عرض مصدر جدول معاملات كلبسش-غوردان

{{يتيمة|تاريخ=ديسمبر 2015}}

{{ترجمة غير مكتملة}}
== الصيغة ==
الصيغة:Formulation

معاملات كلبسش-غوردان هي حلول ل:
:<math>
  |(j_1j_2)jm\rangle = \sum_{m_1=-j_1}^{j_1} \sum_{m_2=-j_2}^{j_2}
  |j_1m_1j_2m_2\rangle \langle j_1j_2;m_1m_2|j_1j_2;jm\rangle
</math>

بشكل مباشر (صريح) إلى:

:<math>
\begin{align}
\langle j_1j_2;m_1m_2|j_1j_2;jm\rangle = \ 
&\delta_{m,m_1+m_2} \sqrt{\frac{(2j+1)(j+j_1-j_2)!(j-j_1+j_2)!(j_1+j_2-j)!}{(j_1+j_2+j+1)!}}\ \times \\
&\sqrt{(j+m)!(j-m)!(j_1-m_1)!(j_1+m_1)!(j_2-m_2)!(j_2+m_2)!}\ \times \\
&\sum_k \frac{(-1)^k}{k!(j_1+j_2-j-k)!(j_1-m_1-k)!(j_2+m_2-k)!(j-j_2+m_1+k)!(j-j_1-m_2+k)!}.
\end{align}
</math>

The summation is extended over all integer {{mvar|k}} for which the argument of every factorial is nonnegative.<ref>(2.41), p. 172, ''Quantum Mechanics: Foundations and Applications'', Arno Bohm, M. Loewe, New York: Springer-Verlag, 3rd ed., 1993, ISBN 0-387-95330-2.</ref>

For brevity, solutions with {{تعبير رياضي|''m'' < 0}} and {{تعبير رياضي|''j''<sub>1</sub> < ''j''<sub>2</sub>}} are omitted. They may be calculated using the simple relations

:<math>\langle j_1j_2;m_1m_2|j_1j_2;jm\rangle=(-1)^{j-j_1-j_2}\langle j_1j_2;-m_1,-m_2|j_1j_2;j,-m\rangle</math> .

و

:<math>\langle j_1j_2;m_1m_2|j_1j_2;jm\rangle=(-1)^{j-j_1-j_2} \langle j_2j_1;m_2m_1|j_2j_1;jm\rangle</math> .

== القائمة الكاملة <ref>{{استشهاد بكتاب|الأخير=Weisbluth|الأول=Michael|عنوان=Atoms and molecules|مسار=https://archive.org/details/atomsmolecules0000weis|سنة=1978|ناشر=ACADEMIC PRESS|ردمك=0-12-744450-5|صفحة=[https://archive.org/details/atomsmolecules0000weis/page/28 28]}} Table 1.4 resumes the most common.</ref> ==

=== {{تعبير رياضي|1=&nbsp;''j''<sub>2</sub>=0}} ===
عندما تكون ''j''<sub>2</sub>=0، فإن معاملات كلبسش-غوردان تعطي
<math>\delta_{j,j_1}\delta_{m,m_1}</math> .

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>={{كسر|1|2}}, ''j''<sub>2</sub>={{كسر|1|2}}}} ===

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=1}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 1
|----- valign="center" align="center"
! {{كسر|1|2}},&nbsp;{{كسر|1|2}} 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=0}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 1 
! 0
|----- valign="center" align="center"
! {{كسر|1|2}},&nbsp;-{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{1}{2}}\!\,</math>
|----- valign="center" align="center"
! -{{كسر|1|2}},&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>-\sqrt{\frac{1}{2}}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>=1, ''j''<sub>2</sub>={{كسر|1|2}}}} ===

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''={{كسر|3|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|3|2}}
|----- valign="center" align="center"
! 1,&nbsp;{{كسر|1|2}} 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''={{كسر|1|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|3|2}} 
! {{كسر|1|2}}
|----- valign="center" align="center"
! 1,&nbsp;-{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{3}}\!\,</math>
| <math>\sqrt{\frac{2}{3}}\!\,</math>
|----- valign="center" align="center"
! 0,&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{2}{3}}\!\,</math>
| <math>-\sqrt{\frac{1}{3}}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>=1, ''j''<sub>2</sub>=1}} ===

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=2}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 2
|----- valign="center" align="center"
! 1,&nbsp;1 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=1}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 2 
! 1
|----- valign="center" align="center"
! 1,&nbsp;0 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{1}{2}}\!\,</math>
|----- valign="center" align="center"
! 0,&nbsp;1 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>-\sqrt{\frac{1}{2}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=0}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 2 
! 1 
! 0
|----- valign="center" align="center"
! 1,&nbsp;-1 
| <math>\sqrt{\frac{1}{6}}\!\,</math>
| <math>\sqrt{\frac{1}{2}}\!\,</math> 
| <math>\sqrt{\frac{1}{3}}\!\,</math>
|----- valign="center" align="center"
! 0,&nbsp;0 
| <math>\sqrt{\frac{2}{3}}\!\,</math>
| <math>0\!\,</math>
| <math>-\sqrt{\frac{1}{3}}\!\,</math>
|----- valign="center" align="center"
! -1,&nbsp;1 
| <math>\sqrt{\frac{1}{6}}\!\,</math>
| <math>-\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{1}{3}}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>={{كسر|3|2}}, ''j''<sub>2</sub>={{كسر|1|2}}}} ===

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=2}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 2
|----- valign="center" align="center"
! {{كسر|3|2}},&nbsp;{{كسر|1|2}} 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=1}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 2 
! 1
|----- valign="center" align="center"
! {{كسر|3|2}},&nbsp;-{{كسر|1|2}} 
| <math>\frac{1}{2}\!\,</math>
| <math>\sqrt{\frac{3}{4}}\!\,</math>
|----- valign="center" align="center"
! {{كسر|1|2}},&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{3}{4}}\!\,</math>
| <math>-\frac{1}{2}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=0}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 2 
! 1
|----- valign="center" align="center"
! {{كسر|1|2}},&nbsp;-{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{1}{2}}\!\,</math>
|----- valign="center" align="center"
! -{{كسر|1|2}},&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>-\sqrt{\frac{1}{2}}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>={{كسر|3|2}}, ''j''<sub>2</sub>=1}} ===

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''={{كسر|5|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|5|2}}
|----- valign="center" align="center"
! {{كسر|3|2}},&nbsp;1 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''={{كسر|3|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|5|2}} 
! {{كسر|3|2}}
|----- valign="center" align="center"
! {{كسر|3|2}},&nbsp;0 
| <math>\sqrt{\frac{2}{5}}\!\,</math>
| <math>\sqrt{\frac{3}{5}}\!\,</math>
|----- valign="center" align="center"
! {{كسر|1|2}},&nbsp;1 
| <math>\sqrt{\frac{3}{5}}\!\,</math>
| <math>-\sqrt{\frac{2}{5}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''={{كسر|1|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|5|2}} 
! {{كسر|3|2}} 
! {{كسر|1|2}}
|----- valign="center" align="center"
! {{كسر|3|2}},&nbsp;-1
| <math>\sqrt{\frac{1}{10}}\!\,</math>
| <math>\sqrt{\frac{2}{5}}\!\,</math> 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
|----- valign="center" align="center"
! {{كسر|1|2}},&nbsp;0 
| <math>\sqrt{\frac{3}{5}}\!\,</math>
| <math>\sqrt{\frac{1}{15}}\!\,</math>
| <math>-\sqrt{\frac{1}{3}}\!\,</math>
|----- valign="center" align="center"
! -{{كسر|1|2}},&nbsp;1
| <math>\sqrt{\frac{3}{10}}\!\,</math>
| <math>-\sqrt{\frac{8}{15}}\!\,</math>
| <math>\sqrt{\frac{1}{6}}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>={{كسر|3|2}}, ''j''<sub>2</sub>={{كسر|3|2}}}} ===

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=3}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 3
|----- valign="center" align="center"
! {{كسر|3|2}},&nbsp;{{كسر|3|2}} 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=2}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 3 
! 2
|----- valign="center" align="center"
! {{كسر|3|2}},&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{1}{2}}\!\,</math>
|----- valign="center" align="center"
! {{كسر|1|2}},&nbsp;{{كسر|3|2}} 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>-\sqrt{\frac{1}{2}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=1}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 3 
! 2 
! 1
|----- valign="center" align="center"
! {{كسر|3|2}},&nbsp;-{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{5}}\!\,</math>
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{3}{10}}\!\,</math>
|----- valign="center" align="center"
! {{كسر|1|2}},&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{3}{5}}\!\,</math>
| <math>0\!\,</math>
| <math>-\sqrt{\frac{2}{5}}\!\,</math>
|----- valign="center" align="center"
! -{{كسر|1|2}},&nbsp;{{كسر|3|2}} 
| <math>\sqrt{\frac{1}{5}}\!\,</math>
| <math>-\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{3}{10}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=0}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 3 
! 2 
! 1 
! 0
|----- valign="center" align="center"
! {{كسر|3|2}},&nbsp;-{{كسر|3|2}}
| <math>\sqrt{\frac{1}{20}}\!\,</math>
| <math>\frac{1}{2}\!\,</math>
| <math>\sqrt{\frac{9}{20}}\!\,</math>
| <math>\frac{1}{2}\!\,</math>
|----- valign="center" align="center"
! {{كسر|1|2}},&nbsp;-{{كسر|1|2}}
| <math>\sqrt{\frac{9}{20}}\!\,</math>
| <math>\frac{1}{2}\!\,</math>
| <math>-\sqrt{\frac{1}{20}}\!\,</math>
| <math>-\frac{1}{2}\!\,</math>
|----- valign="center" align="center"
! -{{كسر|1|2}},&nbsp;{{كسر|1|2}}
| <math>\sqrt{\frac{9}{20}}\!\,</math>
| <math>-\frac{1}{2}\!\,</math>
| <math>-\sqrt{\frac{1}{20}}\!\,</math>
| <math>\frac{1}{2}\!\,</math>
|----- valign="center" align="center"
! -{{كسر|3|2}},&nbsp;{{كسر|3|2}}
| <math>\sqrt{\frac{1}{20}}\!\,</math>
| <math>-\frac{1}{2}\!\,</math>
| <math>\sqrt{\frac{9}{20}}\!\,</math>
| <math>-\frac{1}{2}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>=2, ''j''<sub>2</sub>={{كسر|1|2}}}} ===

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''={{كسر|5|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|5|2}}
|----- valign="center" align="center"
! 2,&nbsp;{{كسر|1|2}} 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''={{كسر|3|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|5|2}} 
! {{كسر|3|2}}
|----- valign="center" align="center"
! 2,&nbsp;-{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{5}}\!\,</math>
| <math>\sqrt{\frac{4}{5}}\!\,</math>
|----- valign="center" align="center"
! 1,&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{4}{5}}\!\,</math>
| <math>-\sqrt{\frac{1}{5}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''={{كسر|1|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|5|2}} 
! {{كسر|3|2}}
|----- valign="center" align="center"
! 1,&nbsp;-{{كسر|1|2}} 
| <math>\sqrt{\frac{2}{5}}\!\,</math>
| <math>\sqrt{\frac{3}{5}}\!\,</math>
|----- valign="center" align="center"
! 0,&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{3}{5}}\!\,</math>
| <math>-\sqrt{\frac{2}{5}}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>=2, ''j''<sub>2</sub>=1}} ===

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=3}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 3
|----- valign="center" align="center"
! 2,&nbsp;1 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=2}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 3 
! 2
|----- valign="center" align="center"
! 2,&nbsp;0 
| <math>\sqrt{\frac{1}{3}}\!\,</math>
| <math>\sqrt{\frac{2}{3}}\!\,</math>
|----- valign="center" align="center"
! 1,&nbsp;1 
| <math>\sqrt{\frac{2}{3}}\!\,</math>
| <math>-\sqrt{\frac{1}{3}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=1}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 3 
! 2 
! 1
|----- valign="center" align="center"
! 2,&nbsp;-1
| <math>\sqrt{\frac{1}{15}}\!\,</math>
| <math>\sqrt{\frac{1}{3}}\!\,</math> 
| <math>\sqrt{\frac{3}{5}}\!\,</math>
|----- valign="center" align="center"
! 1,&nbsp;0
| <math>\sqrt{\frac{8}{15}}\!\,</math>
| <math>\sqrt{\frac{1}{6}}\!\,</math>
| <math>-\sqrt{\frac{3}{10}}\!\,</math>
|----- valign="center" align="center"
! 0,&nbsp;1 
| <math>\sqrt{\frac{2}{5}}\!\,</math>
| <math>-\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{1}{10}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=0}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 3 
! 2 
! 1
|----- valign="center" align="center"
! 1,&nbsp;-1 
| <math>\sqrt{\frac{1}{5}}\!\,</math>
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{3}{10}}\!\,</math>
|----- valign="center" align="center"
! 0,&nbsp;0 
| <math>\sqrt{\frac{3}{5}}\!\,</math>
| <math>0\!\,</math>
| <math>-\sqrt{\frac{2}{5}}\!\,</math>
|----- valign="center" align="center"
! -1,&nbsp;1 
| <math>\sqrt{\frac{1}{5}}\!\,</math>
| <math>-\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{3}{10}}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>=2, ''j''<sub>2</sub>={{كسر|3|2}}}} ===

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''={{كسر|7|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|7|2}}
|----- valign="center" align="center"
! 2,&nbsp;{{كسر|3|2}} 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''={{كسر|5|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|7|2}} 
! {{كسر|5|2}}
|----- valign="center" align="center"
! 2,&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{3}{7}}\!\,</math>
| <math>\sqrt{\frac{4}{7}}\!\,</math>
|----- valign="center" align="center"
! 1,&nbsp;{{كسر|3|2}} 
| <math>\sqrt{\frac{4}{7}}\!\,</math>
| <math>-\sqrt{\frac{3}{7}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''={{كسر|3|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|7|2}} 
! {{كسر|5|2}} 
! {{كسر|3|2}}
|----- valign="center" align="center"
! 2,&nbsp;-{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{7}}\!\,</math>
| <math>\sqrt{\frac{16}{35}}\!\,</math>
| <math>\sqrt{\frac{2}{5}}\!\,</math>
|----- valign="center" align="center"
! 1,&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{4}{7}}\!\,</math>
| <math>\sqrt{\frac{1}{35}}\!\,</math>
| <math>-\sqrt{\frac{2}{5}}\!\,</math>
|----- valign="center" align="center"
! 0,&nbsp;{{كسر|3|2}} 
| <math>\sqrt{\frac{2}{7}}\!\,</math>
| <math>-\sqrt{\frac{18}{35}}\!\,</math>
| <math>\sqrt{\frac{1}{5}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''={{كسر|1|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|7|2}} 
! {{كسر|5|2}} 
! {{كسر|3|2}} 
! {{كسر|1|2}}
|----- valign="center" align="center"
! 2,&nbsp;-{{كسر|3|2}}
| <math>\sqrt{\frac{1}{35}}\!\,</math>
| <math>\sqrt{\frac{6}{35}}\!\,</math>
| <math>\sqrt{\frac{2}{5}}\!\,</math> 
| <math>\sqrt{\frac{2}{5}}\!\,</math>
|----- valign="center" align="center"
! 1,&nbsp;-{{كسر|1|2}}
| <math>\sqrt{\frac{12}{35}}\!\,</math>
| <math>\sqrt{\frac{5}{14}}\!\,</math>
| <math>0\!\,</math>
| <math>-\sqrt{\frac{3}{10}}\!\,</math>
|----- valign="center" align="center"
! 0,&nbsp;{{كسر|1|2}}
| <math>\sqrt{\frac{18}{35}}\!\,</math>
| <math>-\sqrt{\frac{3}{35}}\!\,</math>
| <math>-\sqrt{\frac{1}{5}}\!\,</math>
| <math>\sqrt{\frac{1}{5}}\!\,</math>
|----- valign="center" align="center"
! -1,&nbsp;{{كسر|3|2}}
| <math>\sqrt{\frac{4}{35}}\!\,</math>
| <math>-\sqrt{\frac{27}{70}}\!\,</math>
| <math>\sqrt{\frac{2}{5}}\!\,</math>
| <math>-\sqrt{\frac{1}{10}}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>=2, ''j''<sub>2</sub>=2}} ===

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=4}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 4
|----- valign="center" align="center"
! 2,&nbsp;2 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=3}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 4 
! 3
|----- valign="center" align="center"
! 2,&nbsp;1 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{1}{2}}\!\,</math>
|----- valign="center" align="center"
! 1,&nbsp;2 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>-\sqrt{\frac{1}{2}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=2}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 4 
! 3 
! 2
|----- valign="center" align="center"
! 2,&nbsp;0
| <math>\sqrt{\frac{3}{14}}\!\,</math>
| <math>\sqrt{\frac{1}{2}}\!\,</math> 
| <math>\sqrt{\frac{2}{7}}\!\,</math>
|----- valign="center" align="center"
! 1,&nbsp;1 
| <math>\sqrt{\frac{4}{7}}\!\,</math>
| <math>0\!\,</math>
| <math>-\sqrt{\frac{3}{7}}\!\,</math>
|----- valign="center" align="center"
! 0,&nbsp;2
| <math>\sqrt{\frac{3}{14}}\!\,</math>
| <math>-\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{2}{7}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center" align="center"
| {{تعبير رياضي|1=''m''=1}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 4 
! 3 
! 2 
! 1
|----- valign="center" align="center"
! 2,&nbsp;-1
| <math>\sqrt{\frac{1}{14}}\!\,</math>
| <math>\sqrt{\frac{3}{10}}\!\,</math>
| <math>\sqrt{\frac{3}{7}}\!\,</math> 
| <math>\sqrt{\frac{1}{5}}\!\,</math>
|----- valign="center" align="center"
! 1,&nbsp;0 
| <math>\sqrt{\frac{3}{7}}\!\,</math>
| <math>\sqrt{\frac{1}{5}}\!\,</math>
| <math>-\sqrt{\frac{1}{14}}\!\,</math>
| <math>-\sqrt{\frac{3}{10}}\!\,</math>
|----- valign="center" align="center"
! 0,&nbsp;1 
| <math>\sqrt{\frac{3}{7}}\!\,</math>
| <math>-\sqrt{\frac{1}{5}}\!\,</math>
| <math>-\sqrt{\frac{1}{14}}\!\,</math>
| <math>\sqrt{\frac{3}{10}}\!\,</math>
|----- valign="center"  align="center"
! -1,&nbsp;2
| <math>\sqrt{\frac{1}{14}}\!\,</math>
| <math>-\sqrt{\frac{3}{10}}\!\,</math>
| <math>\sqrt{\frac{3}{7}}\!\,</math>
| <math>-\sqrt{\frac{1}{5}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''=0}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 4 
! 3 
! 2 
! 1
! 0
|----- valign="center"  align="center"
! 2,&nbsp;-2
| <math>\sqrt{\frac{1}{70}}\!\,</math>
| <math>\sqrt{\frac{1}{10}}\!\,</math>
| <math>\sqrt{\frac{2}{7}}\!\,</math> 
| <math>\sqrt{\frac{2}{5}}\!\,</math>
| <math>\sqrt{\frac{1}{5}}\!\,</math>
|----- valign="center"  align="center"
! 1,&nbsp;-1
| <math>\sqrt{\frac{8}{35}}\!\,</math>
| <math>\sqrt{\frac{2}{5}}\!\,</math>
| <math>\sqrt{\frac{1}{14}}\!\,</math>
| <math>-\sqrt{\frac{1}{10}}\!\,</math>
| <math>-\sqrt{\frac{1}{5}}\!\,</math>
|----- valign="center"  align="center"
! 0,&nbsp;0
| <math>\sqrt{\frac{18}{35}}\!\,</math>
| <math>0\!\,</math>
| <math>-\sqrt{\frac{2}{7}}\!\,</math>
| <math>0\!\,</math> 
| <math>\sqrt{\frac{1}{5}}\!\,</math>
|----- valign="center"  align="center"
! -1,&nbsp;1
| <math>\sqrt{\frac{8}{35}}\!\,</math>
| <math>-\sqrt{\frac{2}{5}}\!\,</math>
| <math>\sqrt{\frac{1}{14}}\!\,</math>
| <math>\sqrt{\frac{1}{10}}\!\,</math>
| <math>-\sqrt{\frac{1}{5}}\!\,</math>
|----- valign="center"  align="center"
! -2,&nbsp;2
| <math>\sqrt{\frac{1}{70}}\!\,</math>
| <math>-\sqrt{\frac{1}{10}}\!\,</math>
| <math>\sqrt{\frac{2}{7}}\!\,</math>
| <math>-\sqrt{\frac{2}{5}}\!\,</math>
| <math>\sqrt{\frac{1}{5}}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>={{كسر|5|2}}, ''j''<sub>2</sub>={{كسر|1|2}}}} ===

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''=3}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 3
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;{{كسر|1|2}} 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''=2}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 3 
! 2
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;-{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{6}}\!\,</math>
| <math>\sqrt{\frac{5}{6}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{5}{6}}\!\,</math>
| <math>-\sqrt{\frac{1}{6}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''=1}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 3 
! 2
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;-{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{3}}\!\,</math>
| <math>\sqrt{\frac{2}{3}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|1|2}},&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{2}{3}}\!\,</math>
| <math>-\sqrt{\frac{1}{3}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''=0}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 3 
! 2
|----- valign="center"  align="center"
! {{كسر|1|2}},&nbsp;-{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{1}{2}}\!\,</math>
|----- valign="center"  align="center"
! -{{كسر|1|2}},&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{1}{2}}\!\,</math>
| <math>-\sqrt{\frac{1}{2}}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>={{كسر|5|2}}, ''j''<sub>2</sub>=1}} ===

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''={{كسر|7|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|7|2}}
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;1 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''={{كسر|5|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|7|2}} 
! {{كسر|5|2}}
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;0 
| <math>\sqrt{\frac{2}{7}}\!\,</math>
| <math>\sqrt{\frac{5}{7}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;1 
| <math>\sqrt{\frac{5}{7}}\!\,</math>
| <math>-\sqrt{\frac{2}{7}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''={{كسر|3|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|7|2}} 
! {{كسر|5|2}} 
! {{كسر|3|2}}
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;-1
| <math>\sqrt{\frac{1}{21}}\!\,</math>
| <math>\sqrt{\frac{2}{7}}\!\,</math> 
| <math>\sqrt{\frac{2}{3}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;0
| <math>\sqrt{\frac{10}{21}}\!\,</math>
| <math>\sqrt{\frac{9}{35}}\!\,</math>
| <math>-\sqrt{\frac{4}{15}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|1|2}},&nbsp;1
| <math>\sqrt{\frac{10}{21}}\!\,</math>
| <math>-\sqrt{\frac{16}{35}}\!\,</math>
| <math>\sqrt{\frac{1}{15}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''={{كسر|1|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|7|2}} 
! {{كسر|5|2}} 
! {{كسر|3|2}}
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;-1 
| <math>\sqrt{\frac{1}{7}}\!\,</math>
| <math>\sqrt{\frac{16}{35}}\!\,</math>
| <math>\sqrt{\frac{2}{5}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|1|2}},&nbsp;0 
| <math>\sqrt{\frac{4}{7}}\!\,</math>
| <math>\sqrt{\frac{1}{35}}\!\,</math>
| <math>-\sqrt{\frac{2}{5}}\!\,</math>
|----- valign="center"  align="center"
! -{{كسر|1|2}},&nbsp;1 
| <math>\sqrt{\frac{2}{7}}\!\,</math>
| <math>-\sqrt{\frac{18}{35}}\!\,</math>
| <math>\sqrt{\frac{1}{5}}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>={{كسر|5|2}}, ''j''<sub>2</sub>={{كسر|3|2}}}} ===

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''=4}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 4
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;{{كسر|3|2}} 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''=3}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 4 
! 3
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{3}{8}}\!\,</math>
| <math>\sqrt{\frac{5}{8}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;{{كسر|3|2}} 
| <math>\sqrt{\frac{5}{8}}\!\,</math>
| <math>-\sqrt{\frac{3}{8}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''=2}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 4 
! 3 
! 2
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;-{{كسر|1|2}}
| <math>\sqrt{\frac{3}{28}}\!\,</math>
| <math>\sqrt{\frac{5}{12}}\!\,</math>
| <math>\sqrt{\frac{10}{21}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;{{كسر|1|2}}
| <math>\sqrt{\frac{15}{28}}\!\,</math>
| <math>\sqrt{\frac{1}{12}}\!\,</math>
| <math>-\sqrt{\frac{8}{21}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|1|2}},&nbsp;{{كسر|3|2}}
| <math>\sqrt{\frac{5}{14}}\!\,</math>
| <math>-\sqrt{\frac{1}{2}}\!\,</math>
| <math>\sqrt{\frac{1}{7}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''=1}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 4 
! 3 
! 2 
! 1
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;-{{كسر|3|2}}
| <math>\sqrt{\frac{1}{56}}\!\,</math>
| <math>\sqrt{\frac{1}{8}}\!\,</math>
| <math>\sqrt{\frac{5}{14}}\!\,</math>
| <math>\sqrt{\frac{1}{2}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;-{{كسر|1|2}}
| <math>\sqrt{\frac{15}{56}}\!\,</math>
| <math>\sqrt{\frac{49}{120}}\!\,</math>
| <math>\sqrt{\frac{1}{42}}\!\,</math>
| <math>-\sqrt{\frac{3}{10}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|1|2}},&nbsp;{{كسر|1|2}}
| <math>\sqrt{\frac{15}{28}}\!\,</math>
| <math>-\sqrt{\frac{1}{60}}\!\,</math>
| <math>-\sqrt{\frac{25}{84}}\!\,</math>
| <math>\sqrt{\frac{3}{20}}\!\,</math>
|----- valign="center"  align="center"
! -{{كسر|1|2}},&nbsp;{{كسر|3|2}}
| <math>\sqrt{\frac{5}{28}}\!\,</math>
| <math>-\sqrt{\frac{9}{20}}\!\,</math>
| <math>\sqrt{\frac{9}{28}}\!\,</math>
| <math>-\sqrt{\frac{1}{20}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''=0}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! 4 
! 3 
! 2 
! 1
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;-{{كسر|3|2}}
| <math>\sqrt{\frac{1}{14}}\!\,</math>
| <math>\sqrt{\frac{3}{10}}\!\,</math>
| <math>\sqrt{\frac{3}{7}}\!\,</math> 
| <math>\sqrt{\frac{1}{5}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|1|2}},&nbsp;-{{كسر|1|2}} 
| <math>\sqrt{\frac{3}{7}}\!\,</math>
| <math>\sqrt{\frac{1}{5}}\!\,</math>
| <math>-\sqrt{\frac{1}{14}}\!\,</math>
| <math>-\sqrt{\frac{3}{10}}\!\,</math>
|----- valign="center"  align="center"
! -{{كسر|1|2}},&nbsp;{{كسر|1|2}} 
| <math>\sqrt{\frac{3}{7}}\!\,</math>
| <math>-\sqrt{\frac{1}{5}}\!\,</math>
| <math>-\sqrt{\frac{1}{14}}\!\,</math>
| <math>\sqrt{\frac{3}{10}}\!\,</math>
|----- valign="center"  align="center"
! -{{كسر|3|2}},&nbsp;{{كسر|3|2}}
| <math>\sqrt{\frac{1}{14}}\!\,</math>
| <math>-\sqrt{\frac{3}{10}}\!\,</math>
| <math>\sqrt{\frac{3}{7}}\!\,</math>
| <math>-\sqrt{\frac{1}{5}}\!\,</math>
|}
|}

=== {{تعبير رياضي|1=&nbsp;''j''<sub>1</sub>={{كسر|5|2}}, ''j''<sub>2</sub>=2}} ===

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''={{كسر|9|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|9|2}}
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;2 
| <math>1\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''={{كسر|7|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|9|2}} 
! {{كسر|7|2}}
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;1 
| <math>\frac{2}{3}\!\,</math>
| <math>\sqrt{\frac{5}{9}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;2 
| <math>\sqrt{\frac{5}{9}}\!\,</math>
| <math>-\frac{2}{3}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''={{كسر|5|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|9|2}} 
! {{كسر|7|2}} 
! {{كسر|5|2}}
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;0 
| <math>\sqrt{\frac{1}{6}}\!\,</math>
| <math>\sqrt{\frac{10}{21}}\!\,</math>
| <math>\sqrt{\frac{5}{14}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;1 
| <math>\sqrt{\frac{5}{9}}\!\,</math>
| <math>\sqrt{\frac{1}{63}}\!\,</math>
| <math>-\sqrt{\frac{3}{7}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|1|2}},&nbsp;2
| <math>\sqrt{\frac{5}{18}}\!\,</math>
| <math>-\sqrt{\frac{32}{63}}\!\,</math>
| <math>\sqrt{\frac{3}{14}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''={{كسر|3|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|9|2}} 
! {{كسر|7|2}} 
! {{كسر|5|2}} 
! {{كسر|3|2}}
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;-1
| <math>\sqrt{\frac{1}{21}}\!\,</math>
| <math>\sqrt{\frac{5}{21}}\!\,</math>
| <math>\sqrt{\frac{3}{7}}\!\,</math> 
| <math>\sqrt{\frac{2}{7}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;0
| <math>\sqrt{\frac{5}{14}}\!\,</math>
| <math>\sqrt{\frac{2}{7}}\!\,</math>
| <math>-\sqrt{\frac{1}{70}}\!\,</math>
| <math>-\sqrt{\frac{12}{35}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|1|2}},&nbsp;1
| <math>\sqrt{\frac{10}{21}}\!\,</math>
| <math>-\sqrt{\frac{2}{21}}\!\,</math>
| <math>-\sqrt{\frac{6}{35}}\!\,</math>
| <math>\sqrt{\frac{9}{35}}\!\,</math>
|----- valign="center"  align="center"
! -{{كسر|1|2}},&nbsp;2
| <math>\sqrt{\frac{5}{42}}\!\,</math>
| <math>-\sqrt{\frac{8}{21}}\!\,</math>
| <math>\sqrt{\frac{27}{70}}\!\,</math>
| <math>-\sqrt{\frac{4}{35}}\!\,</math>
|}
|}

{| class="wikitable"
|----- valign="center"  align="center"
| {{تعبير رياضي|1=''m''={{كسر|1|2}}}} 
| {{mvar|j}}
|----- valign="center" 
| {{تعبير رياضي|''m''<sub>1</sub>,&nbsp;''m''<sub>2</sub>}}
|
{| class="wikitable"
|----- valign="center" 
|
 
! {{كسر|9|2}} 
! {{كسر|7|2}} 
! {{كسر|5|2}} 
! {{كسر|3|2}}
! {{كسر|1|2}}
|----- valign="center"  align="center"
! {{كسر|5|2}},&nbsp;-2
| <math>\sqrt{\frac{1}{126}}\!\,</math>
| <math>\sqrt{\frac{4}{63}}\!\,</math>
| <math>\sqrt{\frac{3}{14}}\!\,</math>
| <math>\sqrt{\frac{8}{21}}\!\,</math>
| <math>\sqrt{\frac{1}{3}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|3|2}},&nbsp;-1
| <math>\sqrt{\frac{10}{63}}\!\,</math>
| <math>\sqrt{\frac{121}{315}}\!\,</math>
| <math>\sqrt{\frac{6}{35}}\!\,</math>
| <math>-\sqrt{\frac{2}{105}}\!\,</math>
| <math>-\sqrt{\frac{4}{15}}\!\,</math>
|----- valign="center"  align="center"
! {{كسر|1|2}},&nbsp;0
| <math>\sqrt{\frac{10}{21}}\!\,</math>
| <math>\sqrt{\frac{4}{105}}\!\,</math>
| <math>-\sqrt{\frac{8}{35}}\!\,</math>
| <math>-\sqrt{\frac{2}{35}}\!\,</math>
| <math>\sqrt{\frac{1}{5}}\!\,</math>
|----- valign="center"  align="center"
! -{{كسر|1|2}},&nbsp;1
| <math>\sqrt{\frac{20}{63}}\!\,</math>
| <math>-\sqrt{\frac{14}{45}}\!\,</math>
| <math>0\!\,</math>
| <math>\sqrt{\frac{5}{21}}\!\,</math>
| <math>-\sqrt{\frac{2}{15}}\!\,</math>
|----- valign="center"  align="center"
! -{{كسر|3|2}},&nbsp;2
| <math>\sqrt{\frac{5}{126}}\!\,</math>
| <math>-\sqrt{\frac{64}{315}}\!\,</math>
| <math>\sqrt{\frac{27}{70}}\!\,</math>
| <math>-\sqrt{\frac{32}{105}}\!\,</math>
| <math>\sqrt{\frac{1}{15}}\!\,</math>
|}
|}

== وصلات خارجية ==
* Online, [[جاوة (جزيرة)|جاوة]]-based [http://personal.ph.surrey.ac.uk/~phs3ps/cgjava.html Clebsch-Gordan Coefficient Calculator] by Paul Stevenson
* [http://functions.wolfram.com/HypergeometricFunctions/ClebschGordan/06/01/ Other formulae] for Clebsch–Gordan coefficients.
* [http://homepages.physik.uni-muenchen.de/~vondelft/Papers/ClebschGordan/ Web interface for tabulating SU(N) Clebsch-Gordan coefficients]

== مصادر ومراجع ==
{{مراجع}}

== طالع أيضا ==
* [[نظام عد]]
* [[جدول القواسم]]
* [[جدول التفكيك إلى عوامل أولية]]
{{شريط بوابات|رياضيات}}

[[تصنيف:قوائم متعلقة بالرياضيات]]
[[تصنيف:حساب]]
[[تصنيف:جداول رياضيات]]