International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 39, Pages 2091-2096
doi:10.1155/S016117120430743X

Fourier transform and distributional representation of the gamma function leading to some new identities

M. Aslam Chaudhry1 and Asghar Qadir1,2

1Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Rawalpindi, Pakistan

Received 30 July 2003

Copyright © 2004 M. Aslam Chaudhry and Asghar Qadir. 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.

Abstract

We present a Fourier transform representation of the gamma functions, which leads naturally to a distributional representation for them. Both of these representations lead to new identities for the integrals of gamma functions multiplied by other functions, which are also presented here.