International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 1, Pages 143-153

Some multiple Gaussian hypergeometric generalizations of Buschman-Srivastava theorem

M. I. Qureshi,1 M. Sadiq Khan,2 and M. A. Pathan3

1Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi 110025, India
2Department of Mathematics, Shibli National College, Azamgarh 276 001, Uttar Pradesh, India
3Department of Mathematics, Aligarh Muslim University, Aligarh 202002, Uttar Pradesh, India

Received 29 June 2003

Copyright © 2005 M. I. Qureshi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.