Some results on the $P_{v,2n}$, $K_{v,n}$, and $H_{v,n}$-integral transforms

Abstract

In this paper, the authors consider the Pv,2n -transform, the Gn -transform, and the Kv,n -transform as generalizations of the Widder potential transform, the Glasser transform, and the Kv -transform, respectively. Many identities involving these transforms are given. A number of new Parseval-Goldstein type identities are obtained for these and many other well-known integral transforms. Some useful corollaries for evaluating infinite integrals of special functions are presented. Illustrative examples are given for the results.

Some Relations for the Generalized G ̃n,P ̃n Integral Transforms and Riemann-Liouville, Weyl Integral Operators

“…Recently, the relations between fractional integral operators and classical integral transforms were given. New Parseval-Goldstein type identities were obtained [4][5][6].…”

“…Two generalizations of fractional integrals are defined. New identities for two new generalized fractional integrals and generalized integral transforms [4,8] are obtained. Some definitions will be given, before the main results.…”

New identities on some generalized integral transforms and their applications

“…Dernek and Aylikci defined in [5,6] the P v,2n -transform, the P 2n -transform and the G 2n -transform as generalizations of the Widder Potential transform and the Glasser transform (see [7,13,16]) respectively as follows:…”

“…The F s,n -transform and the F c,n -transform are introduced in [6,8] as generalizations Fourier sine and Fourier cosine transforms,…”

“…The K v,n -transform and the H v,n -transform are defined in [6] as generalizations of the K -transform and the Hankel transform as follows:…”