Journal
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
Volume 24, Issue 10, Pages 807-816Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/10652469.2012.761613
Keywords
Euclidean space; polyharmonic equation; fundamental solution; Gegenbauer polynomials; associated Legendre functions
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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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