Formula:10405

Digital Library of Mathematical Functions ID 34.2.E4

${\displaystyle{\displaystyle\mathit{3j}{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}}={(-1)^{j_{1}-j_{2}-m_{3}}}\Delta(j_{1}j_{2}j_{3})\left((j_{1}+m_{1})!(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!(j_{3}+m_{3})!(j_{3}-m_{3})!\right)^{\frac{1}{2}}\*\sum_{s}\frac{(-1)^{s}}{s!(j_{1}+j_{2}-j_{3}-s)!(j_{1}-m_{1}-s)!(j_{2}+m_{2}-s)!(j_{3}-j_{2}+m_{1}+s)!(j_{3}-j_{1}-m_{2}+s)!},}}$

Symbols List

• ${\displaystyle{\displaystyle!}}$:
• ${\displaystyle{\displaystyle j,j_{r}}}$: non-negative integers or non-negative integers plus one half.
• ${\displaystyle{\displaystyle\Delta(j_{1}j_{2}j_{3})}}$: product (locally)
• ${\displaystyle{\displaystyle s}}$: nonnegative integer
 

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