Paper: Generalizations of generating functions for basic hypergeometric orthogonal polynomials

Cohl, H. S., Costas-Santos, R. S., Hwang, P. R. and Wakhare, T. V. Open Journal of Mathematical Sciences. Accepted in 2021

PSR PRESS (Pakistan) | ISSN: 2616-4906 | JCR® 2021 Impact Factor: n/a

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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