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PUBLICATIONS

Generalizations of generating functions for basic hypergeometric orthogonal polynomials

Published

Author(s)

Howard Cohl, Philbert Hwang, Roberto S. Costas-Santos

Abstract

We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one extra free parameter to them. In particular, we generalize generating functions for the continuous q-ultraspherical/Rogers, little q-Laguerre/Wall, and q-Laguerre polynomials. Depending on what type of orthogonality these polynomials satisfy, we derive corresponding definite integrals, infinite series, bilateral infinite series, and q-integrals.
Citation
Open Journal of Mathematical Sciences
Volume
6
Pub Type
Journals

Download Paper

DOI Link

Keywords

Basic hypergeometric series, Basic hypergeometric orthogonal polynomials, Generating functions, Connection coefficients, Eigenfunction expansions, Definite integrals, Infinite series, Bilateral infinite series, q-integrals.
Modeling and simulation research

Citation

Cohl, H. , Hwang, P. and Costas-Santos, R. (2022), Generalizations of generating functions for basic hypergeometric orthogonal polynomials, Open Journal of Mathematical Sciences, [online], https://doi.org/10.30538/oms2022.0190 (Accessed October 14, 2025)

Issues

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Created November 19, 2022, Updated August 20, 2024
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