Abstract
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.
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