Parameter Augmentation for Basic Hypergeometric Series, II

In a previous paper, we explored the idea of parameter augmentation for basic hypergeometric series, which provides a method of provingq-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 forq-integrals such as the Askey–Wilson integral, the Nassrallah–Rahman integral, theq-integral form of Sears transformation, and Gasperʹs 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 knownq-summation and transformation formulas. A brief treatment of the Rogers–Szegö polynomials is also given.