q-difference equations for Askey-Wilson type integrals via q-polynomials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:452

Article

Cao, Jian^1,2  Niu, Da-Wei³ 

[1] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China

[2] Univ Lyon 1, CNRS, Inst Camille Jordan, UMR 5208, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France

[3] East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

关键词: Askey-Wilson integral;    q-difference equation;    Generating function;    q-orthogonal polynomials;    q-series;   

DOI  :  10.1016/j.jmaa.2017.03.028

来源: Elsevier

【 摘 要 】

In this paper, we show how to deduce Askey-Wilson type integrals by the method of q-difference equation. In addition, we construct the relation between bilinear generating functions and solutions of q-difference equation. More over, we generalize Bailey's 6 psi 6 summation from the perspective of q-integral by the method of q-difference equation. At last, we deduce U(n + 1) type generating functions for Al-Salam-Carlitz polynomials by the method of q-difference equation. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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