Some multiple Gaussian hypergeometric generalizations of Buschman-Srivastava theorem

Abstract

Some generalizations of Bailey's theorem involving the product of two Kummer functions 1F1 are obtained by using Watson's theorem and Srivastava's identities. Its special cases yield various new transformations and reduction formulae involving Pathan's quadruple hypergeometric functions Fp(4), Srivastava's triple and quadruple hypergeometric functions F(3), F(4), Lauricella's quadruple hypergeometric function FA(4), Exton's multiple hypergeometric functions XE:G;HA:B;D, K10, K13, X8, (k)H2(n), (k)H4(n), Erdélyi's multiple hypergeometric function Hn,k, Khan and Pathan's triple hypergeometric function H4(P), Kampé de Fériet's double hypergeometric function FE:G;HA:B;D, Appell's double hypergeometric function of the second kind F2, and the Srivastava-Daoust function FD:E(1);E(2);…;E(n)A:B(1);B(2);…;B(n). Some known results of Buschman, Srivastava, and Bailey are obtained.