Abstract

In this paper a Parseval-Goldstein type theorem involving the Widder potential transform and a Laplace type integral transform is given. The theorem is then shown to yield a relationship between the 𝒦-transform and the Laplace type integral transform. The theorem yields some simple algorithms for evaluating infinite integrals. Using the theorem and its results, a number of new infinite integrals of elementary and special functions are presented. Some illustrative examples are also given.