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International Journal of Mathematics and Mathematical Sciences
Volume 23, Issue 2, Pages 99-102

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 Hindawi Publishing Corporation. 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.


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 identity0sin(ax)/xdx=π/2 is a special case of our main result.