Geodesic
Finite differences, Clebsch–Gordan coefficients, and hypergeometric functions
Teoretičeskaâ i matematičeskaâ fizika, Tome 17 (1973) no. 1, pp. 67-78 
V. P. Karassiov; L. A. Shelepin. Finite differences, Clebsch–Gordan coefficients, and hypergeometric functions. Teoretičeskaâ i matematičeskaâ fizika, Tome 17 (1973) no. 1, pp. 67-78. http://geodesic.mathdoc.fr/item/TMF_1973_17_1_a6/
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     author = {V. P. Karassiov and L. A. Shelepin},
     title = {Finite differences, {Clebsch{\textendash}Gordan} coefficients, and hypergeometric functions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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