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Generalizations of generating functions for basic hypergeometric orthogonal polynomials

Research paper by Howard S. Cohl, Roberto S. Costas-Santos, Philbert R. Hwang

Indexed on: 05 Nov '14Published on: 05 Nov '14Published in: Mathematics - Classical Analysis and ODEs



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 Askey-Wilson, Rogers/continuous $q$-ultrapherical, 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.