Some reduction formulas for multiple hypergeometric series (Q1103078)

Motivated by an earlier work of \textit{M. E. Cohen} [Proc. Am. Math. Soc. 57, 271-275 (1976; Zbl 0325.33007)], the authors prove a general theorem on the reducibility of a certain multiple series and apply it to derive numerous reduction formulas for hypergeometric functions of several variables. Some applications of this theorem, involving Jacobi polynomials, are also presented. Reduction formulas involving various multiple Gaussian hypergeometric series [considered by \textit{H. M. Srivastava} and \textit{P. W. Karlsson}, Multiple Gaussian hypergeometric series (1985; Zbl 0552.33001)] are also considered.