Identities for the Ln-transform, the L2n-transform and the P2n transform and their applications

TL;DR

This paper introduces new integral transforms generalizing classical transforms, explores their relationships, and derives identities useful for evaluating integrals of special functions, with illustrative examples.

Contribution

The paper presents novel integral transforms (Ln, L2n, P2n) and establishes their relationships and identities, expanding tools for integral evaluation.

Findings

Second iterate of L2n-transform equals P2n-transform

Derived new Parseval-Goldstein type identities

Provided examples for evaluating integrals of special functions

Abstract

In the present paper, the authors introduce several new integral transforms including the Ln-transform, the L2n-transform and P2n-transform generalizations of the classical Laplace transform and the classical Stieltjes transform as respectively. It is shown that the second iterate of the L2n-transform is essentially the P2n-transform. Using this relationship, a few new Parseval-Goldstein type identities are obtained. The theorem and the lemmas that are proven in this article are new useful relations for evaluating infinite integrals of special functions. Some related illustrative examples are also given.