On a generalization of the generating function for Gegenbauer polynomials

DOI10.1080/10652469.2012.761613zbMath1280.35003arXiv1105.2735OpenAlexW2963091096MaRDI QIDQ2867908

Howard S. Cohl

Publication date: 20 December 2013

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.2735

zbMATH Keywords

polyharmonic equationassociated Legendre functionsHeine's reciprocal square-root identity

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Hyperbolic and Kobayashi hyperbolic manifolds (32Q45) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Classical hypergeometric functions, ({}_2F_1) (33C05) Higher-order elliptic equations (35J30) Potential theory on Riemannian manifolds and other spaces (31C12)

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Uses Software

• DLMF

Cites Work

• Unnamed Item
• Green's functions for polynomials in the Laplacian
• Alternative approach to the solution of the momentum-space Schrödinger equation for bound states of the N-dimensional Coulomb problem
• Some integrals and series involving the Gegenbauer polynomials and the Legendre functions on the cut (−1, 1)
• Some properties of hyperspherical harmonics
• Expansion formulas and addition theorems for Gegenbauer functions
• Generalization of Laplace's Expansion to Arbitrary Powers and Functions of the Distance between Two Points

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