A note on generalized q-difference equations for q-beta and Andrews-Askey integral

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:412

Article

Cao, Jian^1,2 

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

[2] Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China

关键词: q-difference equation;    q-exponential operator;    Ramanujan's q-beta integral;    Andrews-Askey integral;    Generating function;    Al-Salam-Carlitz polynomial;    q-Chu-Vandermonde formula;   

DOI  :  10.1016/j.jmaa.2013.11.027

来源: Elsevier

【 摘 要 】

Two q-difference equations with solutions expressed by q-exponential operator identities are investigated. As applications, two extensions of Ramanujan's formulas for q-beta integral are given, two generalizations of Andrews-Askey integral are obtained. In addition, generating functions for generalized Al-Salam-Carlitz polynomials are deduced. At last, a generalized transformation identity is gained. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free