{ j 1 j 2 j 3 \ 1 2 j 3 - 1 2 j 2 - 1 2 } = ( - 1 ) J ( ( j 2 + j 3 - j 1 ) ( j 1 + j 2 + j 3 + 1 ) 2 j 2 ( 2 j 2 + 1 ) 2 j 3 ( 2 j 3 + 1 ) ) 1 2 \begin{Bmatrix}j_{1}&j_{2}&j_{3}\ \frac{1}{2}&j_{3}-\frac{1}{2}&j_{2}-\frac{1}{2}\end{Bmatrix}=(-1)^{J}\left(\frac{(j_{2}+j_{3}-j_{1})(j_{1}+j_{2}+j_{3}+1)}{2j_{2}(2j_{2}+1)2j_{3}(2j_{3}+1)}\right)^{\frac{1}{2}}