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Addition theorems for Legendre functions as corollaries of an addition theorem for Gegenbauer polynomials

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Abstract

Proofs are given for addition theorems for Legendre functions with arbitrary upper and lower indices, based solely on an addition theorem for Gegenbauer polynomials. New versions of these and other similar theorems are given, both in the form of sums and of integrals.

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Authors and Affiliations

  1. All-Union Institute of Scientific and Technological Information, USSR

    N. N. Beloozerov

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  1. N. N. Beloozerov
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Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 321–330, September, 1976.

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Beloozerov, N.N. Addition theorems for Legendre functions as corollaries of an addition theorem for Gegenbauer polynomials. Mathematical Notes of the Academy of Sciences of the USSR 20, 740–745 (1976). https://doi.org/10.1007/BF01097241

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  • DOI: https://doi.org/10.1007/BF01097241

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