Laplace transform of certain functions with applications

M Aslam Chaudhry

doi:10.1155/s0161171200001150

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 is a special case of our main result.

Highlights

The Laplace transform of the functions tν (1 + t)β, Re ν > −1, can be expressed in terms of the confluent hypergeometric function ψ [4, p. 268]
Some special cases of the Laplace transform of these functions are listed in the literature [2, 3]
We exploit the relationship between the Whittaker and the confluent hypergeometric functions to express the Laplace transform of certain functions in terms of the Whittaker functions

Summary

Introduction

The Laplace transform of the functions tν (1 + t)β, Re ν > −1, can be expressed in terms of the confluent hypergeometric function ψ [4, p. 268]. Π /2 is a special case of our main result. The Laplace transform of the functions tν (1 + t)β, Re ν > −1, can be expressed in terms of the confluent hypergeometric function ψ [4, p. Some special cases of the Laplace transform of these functions are listed in the literature [2, 3].

Results

Conclusion