On a generalization of the generating function for Gegenbauer polynomials
Classical Analysis and ODEs
2013-01-18 v3 Mathematical Physics
Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.1105.2735,
title = {On a generalization of the generating function for Gegenbauer polynomials},
author = {Howard S. Cohl},
journal= {arXiv preprint arXiv:1105.2735},
year = {2013}
}