Notes on $q$-Partial Differential Equations for $q$-Laguerre Polynomials and Little $q$-Jacobi Polynomials-Reference-Cited by-同舟云学术

Notes on $q$-Partial Differential Equations for $q$-Laguerre Polynomials and Little $q$-Jacobi Polynomials

Published:2024-06-30 Issue:2 Volume:7 Page:59-76
ISSN:2645-8845
Container-title:Fundamental Journal of Mathematics and Applications
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Author:

Bao Qi¹^ORCID,Yang Dunkun¹^ORCID

Affiliation:

1. East China Normal University

Abstract

This article defines two common $q$-orthogonal polynomials: homogeneous $q$-Laguerre polynomials and homogeneous little $q$-Jacobi polynomials. They can be viewed separately as solutions to two $q$-partial differential equations. Furthermore, an analytic function satisfies a certain system of $q$-partial differential equations if and only if it can be expanded in terms of homogeneous $q$-Laguerre polynomials or homogeneous little $q$-Jacobi polynomials. As applications, several generalized Ramanujan $q$-beta integrals and Andrews-Askey integrals are obtained.

Publisher

Fundamental Journal of Mathematics and Applications

Reference61 articles.

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