Generalizations of generating functions for basic hypergeometric orthogonal polynomials

2014/11/05 by Howard S. Cohl, Cohl, Howard S., Roberto S. Costas-Santos +5
Mathematics · #05A15 #30E20 #33C20 #33C45 #34L10 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1411.1371

openalex publication_date 2014/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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