Laplace transform of certain functions with applications
type: Item
instance of: scholarly article
title: Laplace transform of certain functions with applications
zbMATH Open document ID: 0949.60038
DOI: 10.1155/S0161171200001150
author: M. Aslam Chaudhry
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2000-12-03T00:00:00Z
full work available at URL: https://eudml.org/doc/48578
review text: Summary: The Laplace transform of the functions \(t^\nu(1+ t)^\beta\), \(\text{Re} \nu>-1\), 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 \(\int^\infty_0 \sin(ax)/x dx=\pi/2\) is a special case of our main result.
Mathematics Subject Classification ID: 60E10
zbMATH DE Number: 1441869
zbMATH Keywords: Laplace transforms
zbMATH Keywords: probability density functions
zbMATH Keywords: Whittaker functions
MaRDI profile type: Publication
OpenAlex ID: W2158278422
description: scientific article; zbMATH DE number 1441869