I'm trying to take advantage of a particular identity for the sum of the product of three Clebsch-Gordan coefficients, however, the present form of my equation is slightly different. Is there a symmetry relation that will allow me to change:

$\sum_{\alpha\beta\delta}C_{a\alpha b\beta}^{c\gamma}C_{d\delta b\beta}^{e\epsilon}C_{d\delta f\phi}^{a\alpha}$

Into:

$\sum_{\alpha\beta\delta}C_{a\alpha b\beta}^{c\gamma}C_{d\delta b\beta}^{e\epsilon}C_{a\alpha f\phi}^{d\delta}$

Notice I need to swap j2m2 with jm in the last Clebsh-Gordan coefficient. Does anyone know a way to do this?

Note: My notation follows that of Varshalovich, $C_{j_1 m_1 j_2 m_2}^{jm}$

This post imported from StackExchange Physics at 2014-04-01 05:47 (UCT), posted by SE-user okj