A generalization of the Widder potential transform and applications

TL;DR

This paper introduces a new generalized integral transform called the al P_{ u,2} transform, extending the Widder potential and Glasser transforms, and explores their identities and applications in evaluating integrals of special functions.

Contribution

It presents the al P_{ u,2} transform as a novel generalization obtained via iteration of the al ext{L}_2 transform, along with new identities and applications.

Findings

Derived new Parseval-Goldstein type identities

Provided methods for evaluating integrals of special functions

Illustrated results with concrete examples

Abstract

In the present paper the authors consider the $\mathcal{P}_{\nu,2}$-transform as a generalization of the Widder potential transform and the Glasser transform. The $\mathcal{P}_{\nu,2}$-transform is obtained as an iteration of the the $\mathcal{L}_{2}$-transform with itself. Many identities involving these transforms are given. By making use of these identities, a number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.