Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms

TL;DR

This paper introduces new Parseval-Goldstein type identities for generalized integral transforms, enabling the evaluation of improper integrals involving fundamental and special functions.

Contribution

It establishes novel identities for generalized transforms like the al_{\u03b1,} and Stieltjes transforms, expanding the theoretical framework.

Findings

Derived new Parseval-Goldstein identities for generalized transforms

Evaluated improper integrals of special functions using these identities

Extended classical integral transform relations

Abstract

In this work, we establish some Parseval-Goldstein type identities and relations that include various new generalized integral transforms such as $\mathcal{L}_{\alpha,\mu}$-transform and generalized Stieltjes transform. In addition, we evaluated improper integrals of some fundamental and special functions using our results.