International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 2, Pages 99-102
doi:10.1155/S0161171200001150
Laplace transform of certain functions with applications
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
Received 21 June 1993
Copyright © 2000 M. Aslam Chaudhry. 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
The Laplace transform of the functions tν(1+t)β, Reν>−1, is expressed in terms of Whittaker functions. This
expression is exploited to evaluate infinite integrals involving
products of Bessel functions, powers, exponentials, and
Whittaker functions. Some special cases of the result
are discussed. It is also demonstrated that the famous identity∫0∞sin (ax)/x dx=π/2 is a special case of our
main result.