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Publication Citation: Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals

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Author(s): Howard S. Cohl; Connor M. MacKenzie;
Title: Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals
Published: April 30, 2013
Abstract: We generalize generating functions for hypergeometric orthogonal polynomials, namely Jacobi, Gegenbauer, Laguerre, and Wilson polynomials. These generalizations of generating functions are accomplished through series rearrangement using connection relations with one free parameter for these orthogonal polynomials. We also use orthogonality relations to determine corresponding definite integrals.
Citation: Journal of Mathematical Analysis and Applications
Volume: 407
Issue: 2
Pages: pp. 211 - 225
Keywords: Orthogonal polynomials; Generating functions; Connection coefficients; Generalized hypergeometric functions; Eigenfunction expansions; Definite integrals
Research Areas: Modeling
DOI: http://dx.doi.org/10.1016/j.jmaa.2013.04.067  (Note: May link to a non-U.S. Government webpage)
PDF version: PDF Document Click here to retrieve PDF version of paper (448KB)