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arXiv · 1105.2735

On a generalization of the generating function for Gegenbauer polynomials

Howard S. Cohl
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Abstract

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 our expansion represents a generalization of several previously derived formulae such as Heine's formula and Heine's reciprocal square-root identity. We also show how this expansion can be used to compute hyperspherical harmonic expansions for power-law fundamental solutions of the polyharmonic equation.

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Howard S. Cohl. 2011-05-13. On a generalization of the generating function for Gegenbauer polynomials. https://arxiv.org/abs/1105.2735

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