Some results for q-functions of many variables II

This is a continuation of [19], where we presented an extension of the q-hypergeometric function with connection to the title of this paper. In chapter one we present some quadratic q − hypergeometric transformations, to give more examples of this extension. In chapter two, systems of partial q-difference equations for the q-Appell and q-Lauricella functions are presented in the authors notation. Other attempts to find these equations were made by Jackson. It turns out that these q-difference equations can be written in many equivalent forms, which gives rise to the notion of equivalence class for q-difference equations. In chapter three q-analogues of expansion formulas by Chaundy [11] and Burchnall & Chaundy [9] are found. In the process we obtain a corrected version of [26, (55) p.79]. In chapter four we find an expan-sion formula for a Φ 2:1 2:0 function by using Jackson’s sum of a terminating very-well-poised balanced 8φ7 series. We also find the corresponding q-binomial identity