Parameter Augmentation for Basic Hypergeometric Series, II

William Y. C. Chen and Zhi-Guo Liu

  Abstract:  In a previous paper, we explored the idea of parameter augmentation for basic hypergeometric series, which provides a method of proving q-summation 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 q-integrals such as the Askey-Wilson integral, the Nassrallah-Rahman integral, the q-integral form of Sears transformation, and Gasper's formula of the extension of the Askey-Roy integral. The parameter augmentation is realized by another operator, which leads to considerable simplications of some well known q-summa- tion and transformation formulas. A brief treatment of the Rogers-Szegö poly- nomials is also given.