IDENTITIES FOR THE Ln-TRANSFORM, THE L2n-TRANSFORM AND THE P2n TRANSFORM AND THEIR APPLICATIONS

Abstract

In the present paper, the authors introduce several new integral transforms including the L-n-transform, the L-2n-transform and P-2n-transform generalizations of the classical Laplace transform and the classical Stieltjes transform as respectively. It is shown that the second iterate of the L-2n-transform is essentially the P-2n-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.