A note on generalized q-difference equations for q-beta and Andrews-Askey integral
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- 作者：Jian Cao
- 关键词：q-difference equation ; q-exponential operator ; Ramanujan始s q-beta integral ; Andrews&ndash ; Askey integral ; Generating function ; Al-Salam&ndash ; Carlitz polynomial ; q-Chu&ndash ; Vandermonde formula
- 刊名：Journal of Mathematical Analysis and Applications
- 出版年：15 April, 2014
- 年：2014
- 卷：412
- 期：2
- 页码：841-851
- 全文大小：280 K
文摘
Two q-difference equations with solutions expressed by q-exponential operator identities are investigated. As applications, two extensions of Ramanujan始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.