1105.2735 (Howard S. Cohl)

On a generalization of the generating function for Gegenbauer
polynomials    [PDF]

Howard S. Cohl

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.

View original: http://arxiv.org/abs/1105.2735