Generalizations and specializations of generating functions for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with definite integrals

DOI10.7153/jca-03-02zbMath1412.33017arXiv1210.0039OpenAlexW2963491596MaRDI QIDQ3120699

Connor MacKenzie, Howard S. Cohl

Publication date: 5 March 2019

Published in: Journal of Classical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.0039

zbMATH Keywords

generating functionsGauss hypergeometric functioneigenfunction expansionsdefinite integralsothogonal polynomials

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (2)

Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals ⋮ On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions

Uses Software

• DLMF
• Associated Legendre Functions

Cites Work

• A new \texttt{Fortran 90} program to compute regular and irregular associated Legendre functions
• Generating functions of Legendre polynomials: A tribute to Fred Brafman
• Hypergeometric Orthogonal Polynomials and Their q-Analogues
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Generalizations and specializations of generating functions for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with definite integrals