Homogeneous q-partial difference equations and some applications

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• 作者：Jian Cao^a ; ^b ; ^{21caojian@gmail.com} ; ^{cao@math.univ-lyon1.fr}
• 关键词：05A30 ; 11B65 ; 33D15 ; 33D45 ; 39A13
• 刊名：Advances in Applied Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：84
• 期：Complete
• 页码：47-72
• 全文大小：469 K
• 卷排序：84

文摘

In this paper, we show how to prove identities and evaluate integrals by expanding functions in terms of products of the q-hypergeometric polynomials by homogeneous q-partial difference equations, we also generalize some results of Liu (2015) [34] and Cao (2016) [14]. In addition, we generalize multilinear and multiple generating functions for the q-hypergeometric polynomials as applications. Moreover, we deduce some recurring formulas for Ramanujan's integrals, Askey–Roy integrals, Andrews–Askey integrals and moment integrals by the method of homogeneous q-partial difference equations. Finally, we build the relation of Ismail–Zhang type generating functions for the q-hypergeometric polynomials by the method of Ismail and Zhang (2016) [26].