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 TMF, 1973, Volume 17, Number 1, Pages 67–78 (Mi tmf3926)

Finite differences, Clebsch–Gordan coefficients, and hypergeometric functions

V. P. Karassiov, L. A. Shelepin

Abstract: A generalization of the theory of angular momenta is proposed. The generating representation is a representation of finite generalized hypergeometric series by means of operators of finite differences and symbolic powers. A number of new relations are obtained. These generalize the concept of coupling (addition) of angular momenta, in particular, the expression of the Racah coefficients as a sum of products of two Clebsch–Gordan coefficients. The efficiency of the method of finite differences is demonstrated and a study is made of difference differentiation and integration of the Clebsch–Gordan coefficients and $j$-symbols with respect to the angular momenta and their projections. The formulas obtained by this method yield directly numerical values of the $j$-symbols and the other quantities in the theory of angular momenta.

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English version:
Theoretical and Mathematical Physics, 1973, 17:1, 991–998

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Citation: V. P. Karassiov, L. A. Shelepin, “Finite differences, Clebsch–Gordan coefficients, and hypergeometric functions”, TMF, 17:1 (1973), 67–78; Theoret. and Math. Phys., 17:1 (1973), 991–998

Citation in format AMSBIB
\Bibitem{KarShe73} \by V.~P.~Karassiov, L.~A.~Shelepin \paper Finite differences, Clebsch--Gordan coefficients, and hypergeometric functions \jour TMF \yr 1973 \vol 17 \issue 1 \pages 67--78 \mathnet{http://mi.mathnet.ru/tmf3926} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=468788} \zmath{https://zbmath.org/?q=an:0289.33010} \transl \jour Theoret. and Math. Phys. \yr 1973 \vol 17 \issue 1 \pages 991--998 \crossref{https://doi.org/10.1007/BF01035582} 

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This publication is cited in the following articles:
1. V. P. Karassiov, L. A. Shelepin, “Hidden couplings and relationships in the theory of angular momenta”, Theoret. and Math. Phys., 29:1 (1976), 936–942
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