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On a generalization of the generating function for Gegenbauer polynomials (1105.2735v3)
Published 13 May 2011 in math.CA, math-ph, math.AP, and 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.