Parseval–Goldstein type identities involving the ℒ4-transform and the 𝒫4-transform and their applications

Abstract

In the present article the authors introduce several new integral transforms including the ℒ4-transform and the 𝒫4-transform as generalizations of the classical Laplace transform and the classical Stieltjes transform, respectively. It is shown that the second iterate of the ℒ4-transform is essentially the 𝒫4-transform. Using this relationship, a number of new Parseval–Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this article give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustrations of the results presented here.