A generalization of the Widder potential transform and applications

Abstract

In the present paper the authors consider the P ν,2 -transform as a generalization of the Widder potential transform and the Glasser transform. The P ν,2 -transform is obtained as an iteration of the the 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.

New identities on some generalized integral transforms and their applications

“…in the relation (30) of Lemma 2.1, then using the relation (7), the known formulas [14, p.136, Entry (13)] and [14,p.353,Entry(3)] respectively, we have…”

“…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:…”

Some families of the general Mathieu‐type series with associated properties and functional inequalities

“…which was first studied by Rudolf Lipschitz (1832-1903) and Matyáš Lerch (1860-1922) in connection with the Dirichlet's famous theorem on primes in arithmetic progressions (see [ 22 , p. 196]). Various other generalizations of the Hurwitz-Lerch zeta function Φ(z, s, a) have been investigated by many authors (see, e.g., previous studies 8,9,[23][24][25][26][27][28][29] ).…”

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

“…was introduced by Dernek et al [6] as a generalization of the Widder-potential transform and the Glasser transform. If we put v = 1 and v = 1 2 in (1.8), we obtain the Widder potential transform (1.6) and the Glasser transform (1.7), respectively.…”

“…Various Parseval-Goldstein type identities were given (for example in [5][6][7]16,18]) for the L 2 -transform and the L 2n -transform and the Widder potential transform.…”