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

Published

January 15, 2014

Author(s)

Howard S. Cohl, Connor M. MacKenzie

Abstract

In this paper we generalize and specialize generating functions for classical orthogonal polynomials, namely Jacobi, Gegenbauer, Chebyshev and Legendre polynomials. We derive a generalization of the generating function for Gegenbauer polynomials through extension a two element sequence of generating functions for Jacobi polynomials. Specializations of generating functions are accomplished through the re-expression of Gauss hypergeometric functions in terms of less general functions. Definite integrals which correspond to the presented orthogonal polynomial series expansions are also given.

Citation

Journal of Classical Analysis

Volume

3

Issue

1

Pub Type

Journals

Download Paper

https://doi.org/10.7153/jca-03-02

Keywords

Othogonal polynomials, Generating functions, Gauss hypergeometric function, Eigenfunction expansions, Definite integrals

Citation

Cohl, H. and MacKenzie, C. (2014), Generalization and specializations of generating functions for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with definite integrals, Journal of Classical Analysis, [online], https://doi.org/10.7153/jca-03-02 (Accessed October 17, 2025)