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

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Author(s): Howard S. Cohl; Connor M. MacKenzie;
Title: Generalization and specializations of generating functions for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with definite integrals
Published: January 15, 2014
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
Pages: pp. 17 - 33
Keywords: Othogonal polynomials; Generating functions; Gauss hypergeometric function; Eigenfunction expansions; Definite integrals
Research Areas: Modeling
DOI: http://dx.doi.org/10.7153/jca-03-02  (Note: May link to a non-U.S. Government webpage)
PDF version: PDF Document Click here to retrieve PDF version of paper (174KB)