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arXiv · 1411.1371

Generalizations of generating functions for basic hypergeometric orthogonal polynomials

Howard S. Cohl·Roberto S. Costas-Santos·Philbert R. Hwang·Tanay Wakhare
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Abstract

We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one free parameter to them. In particular, we generalize generating functions for the Askey-Wilson, 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.

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Howard S. Cohl, Roberto S. Costas-Santos, Philbert R. Hwang, Tanay Wakhare. 2014-11-05. Generalizations of generating functions for basic hypergeometric orthogonal polynomials. https://arxiv.org/abs/1411.1371

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