Some transformation formulas of 𝑞-hypergeometric series via contour integration

Abstract

We give new methods to obtain certain transformation formulas of q q -hypergeometric series. Our approach uses residue calculus. We apply this method to two categories: hyperbolic and elliptic. We also apply a similar technique to evaluate explicitly a large class of q q -integrals, some of which are related to the work of Gasper (2004) and Ismail and Masson (1994).