9-j Symbol - Reduction To 6j Symbols

Reduction To 6j Symbols

The 9j symbols can be calculated as sums over triple-products of 6j symbols where the summation extends over all x admitted by the triangle conditions in the factors:

\begin{Bmatrix} j_1 & j_2 & j_3\\ j_4 & j_5 & j_6 \\ j_7 & j_8 & j_9 \end{Bmatrix} = \sum_x (-1)^{2x}(2x+1) \begin{Bmatrix} j_1 & j_4 & j_7\\ j_8 & j_9 & x \end{Bmatrix} \begin{Bmatrix} j_2 & j_5 & j_8\\ j_4 & x & j_6 \end{Bmatrix} \begin{Bmatrix} j_3 & j_6 & j_9\\ x & j_1 & j_2 \end{Bmatrix} .

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