SOME TRANSFORMATION AND REDUCTION FORMULAS FOR HYPERGEOMETRIC-SERIES IN SEVERAL VARIABLES

An (alternative) elementary proof of a certain hypergeometric identity, which was posed recently as a problem, leads naturally first to a multiple-series extension of the problem and then also to its related multivariable hypergeometric transformation and summation formulas. A systematic analysis of several general multiple-series identities analogous to these hypergeometric transformations is presented. Many of the general results obtained are shown to unify and extend numerous transformation and reduction formulas for various classes of double and multiple hypergeometric series.