Letters in Mathematical Physics

, Volume 109, Issue 11, pp 2485–2490 | Cite as

Unusual sum rule for Clebsch–Gordan coefficients

  • Jean-Christophe PainEmail author


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.


Clebsch–Gordan coefficients 3j symbols Sum rules 

Mathematics Subject Classification

81R05 20C35 22E70 



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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.CEA, DAM, DIFArpajonFrance

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