Ordinary and basic bivariate hypergeometric transformations associated with the Appell and Kampé de Fériet functions

By means of formal power series method and series rearrangement technique, the authors investigate and establish several ordinary as well as basic (or q-) bivariate hypergeometric transformation and reduction formulas. These latter formulas may be considered as basic (or q-) extensions of some recent results considered by Lee et al. (Internat. J. Comput. Math. 78 (2001) 303–321) and Karlsson et al. (Internat. J. Math. Statist. Sci. 9 (2000) 211–226). The bivariate hypergeometric series, which are considered in this paper, are closely related to the familiar Appell and Kampé de Fériet functions.