On a generalization of the generating function for Gegenbauer\n polynomials

2011/05/13 by Howard S. Cohl, Cohl, Howard S. · 1 citation
Mathematics · Physics and Astronomy · #31C12 #32Q45 #33C05 #35A08 #35J05 #42A16 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.1105.2735

openalex publication_date 2011/05/13 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

A generalization of the generating function for Gegenbauer polynomials is\nintroduced whose coefficients are given in terms of associated Legendre\nfunctions of the second kind. We discuss how our expansion represents a\ngeneralization of several previously derived formulae such as Heine's formula\nand Heine's reciprocal square-root identity. We also show how this expansion\ncan be used to compute hyperspherical harmonic expansions for power-law\nfundamental solutions of the polyharmonic equation.\n

Cited by

• Gravitational signatures of a nonlinear electrodynamics in f(R,T) gravity

Related

• Generalizations and specializations of generating functions for Jacobi,\n Gegenbauer, Chebyshev and Legendre polynomials with definite integrals
• An interesting application of Gegebauer Polynomials
• On the relation between Gegenbauer polynomials and the Ferrers function of the first kind
• Generalizations of generating functions for hypergeometric orthogonal\n polynomials with definite integrals
• Uniform asymptotic expansions for Gegenbauer polynomials and related functions via differential equations having a simple pole