A new sum rule for Clebsch-Gordan coefficients using generalized characters of irreducible representations of the rotation group

Jean-Christophe Pain

Published 2019-04-20Version 1

We present a new sum rule for Clebsch-Gordan coefficients using generalized characters of irreducible representations of the rotation group. The identity is obtained from an integral involving Gegenbauer ultraspherical polynomials. A similar procedure can be applied for other types of integrals of such polynomials, and may therefore lead to the derivation of further new relations.