Parameter Augmentation for Basic Hypergeometric Series, II
William Y. C. Chen and ZhiGuo Liu
Abstract: In a previous paper, we explored the idea of parameter augmentation for basic hypergeometric series, which provides a method of proving qsummation and integral formula based special cases obtained by reducing some parameters to zero. In the present paper, we shall mainly deal with parameter augmentation for qintegrals such as the AskeyWilson integral, the NassrallahRahman integral, the qintegral form of Sears transformation, and Gasper's formula of the extension of the AskeyRoy integral. The parameter augmentation is realized by another operator, which leads to considerable simplications of some well known qsumma tion and transformation formulas. A brief treatment of the RogersSzegö poly nomials is also given.
