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
M.Aslam Chaudhry
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
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.