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Generalizations of generating functions for higher continuous hypergeometric orthogonal polynomials in the Askey scheme

Published

Author(s)

Howard S. Cohl, Hans Volkmer, Michael Baeder

Abstract

We use connection relations and series rearrangement to generalize generating functions for several higher continuous orthogonal polynomials in the Askey scheme, namely the Wilson, continuous dual Hahn, continuous Hahn, and Meixner-Pollaczek polynomials. We also determine corresponding definite integrals using the orthogonality relations for these polynomials.
Citation
Constructive Approximation

Keywords

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

Citation

Cohl, H. , Volkmer, H. and Baeder, M. (2015), Generalizations of generating functions for higher continuous hypergeometric orthogonal polynomials in the Askey scheme, Constructive Approximation, [online], https://doi.org/10.1016/j.jmaa.2015.01.074 (Accessed May 26, 2024)

Issues

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Created February 9, 2015, Updated November 10, 2018