On a generalization of the generating function for Gegenbauer polynomials

Details On a generalization of the generating function for Gegenbauer polynomials On a generalization of the generating function for Gegenbauer polynomials

2011-05-13

arxiv.org/abs/1105.2735v2

Mathematics

Classical Analysis and ODEs

Scientific paper

A generalization of the generating function for Gegenbauer polynomials is introduced whose coefficients are given in terms of associated Legendre functions of the second kind. We discuss how this expansion can be used to compute hyperspherical harmonic expansions for power-law fundamental solutions of the polyharmonic equation. We also show how our series expansion represents a generalization of many previously derived expansions such as Heine's formula and Heine's reciprocal square-root identity.

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