A note on the inverse Laplace transform

Abstract

In this note we show that the method for finding inverse Laplace transform without using integration on the complex plane can be used to find integral representations on the positive real axis for some functions. Furthermore, this inversion method allows us to study the inverse Laplace transform of non-tabulated functions. As application of this procedure, some integral representations are obtained and the inverse Laplace transform of a particular non-tabulated function is discussed.