International Journal of Mathematics and Mathematical Sciences
Volume 25 (2001), Issue 9, Pages 571-586
-function with complex parameters I: existence
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 -function with complex parameters is defined by a
Mellin-Barnes type integral. Necessary and sufficient conditions
under which the integral defining the -function converges
absolutely are established. Some properties, special cases, and an
application to integral transforms are given.