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Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals

Published

Author(s)

Howard S. Cohl, Connor M. MacKenzie

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

Keywords

Orthogonal polynomials, Generating functions, Connection coefficients, Generalized hypergeometric functions, Eigenfunction expansions, Definite integrals

Citation

Cohl, H. and MacKenzie, C. (2013), Generalizations of generating functions for hypergeometric orthogonal polynomials with definite integrals, Journal of Mathematical Analysis and Applications, [online], https://doi.org/10.1016/j.jmaa.2013.04.067 (Accessed May 24, 2024)

Issues

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Created April 30, 2013, Updated November 10, 2018