International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 9, Pages 571-586

H-function with complex parameters I: existence

Fadhel A. Al-Musallam and Vu Kim Tuan

Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Received 10 November 1998; Revised 17 December 1999

Copyright © 2001 Fadhel A. Al-Musallam and Vu Kim Tuan. 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.


An H-function with complex parameters is defined by a Mellin-Barnes type integral. Necessary and sufficient conditions under which the integral defining the H-function converges absolutely are established. Some properties, special cases, and an application to integral transforms are given.