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 December 15, 2024)
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Generalizations of generating functions for basic hypergeometric orthogonal polynomials
Published
Author(s)
, 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
Keywords
Basic hypergeometric series, Basic hypergeometric orthogonal polynomials, Generating functions, Connection coefficients, Eigenfunction expansions, Definite integrals, Infinite series, Bilateral infinite series, q-integrals.
Citation
Issues
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Created November 19, 2022, Updated August 20, 2024