q-differential operator identities and applications

被引：32

作者：

Fang, Jian-Ping ^{[1
]}

机构：

[1] E China Normal Univ, Dept Math, Shanghai 200062, Peoples R China

[2] Huaiyin Teachers Coll, Dept Math, Huaian 223300, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 332卷 / 02期

关键词：

q-series; basic hypergeometric series; q-differential operator; q-ultraspherical polynomials; big q-Laguerre polynomials;

D O I：

10.1016/j.jmaa.2006.10.087

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we construct a new q-exponential operator and obtain some operator identities. Using these operator identities, we give a formal extension of Jackson's (2)Phi(2) transformation formula. A formal extension of Bailey's (3)psi(3) summation and an extension of the Sears terminating balanced (4)Phi(3) transformation formula are also derived by our operator method. In addition, we also derive several interesting a formal extensions involving multiple sum about three terms of Sears (3)Phi(2) transformation formula and Heine's (2)Phi(1) transformation formula. (C) 2006 Elsevier Inc. All rights reserved.

引用

页码：1393 / 1407

页数：15

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