A generalization of the Widder potential transform and applications - DERNEK, AYŞE NEŞE (TAYLOR & FRANCIS LTD, 2011)
In the present paper, the authors consider the P(v,2)-transform as a generalization of the Widder potential transform and the Glasser transform. The P(v,2)-transform is obtained as an iteration of 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 proved 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.
Keywords: Laplace transforms; L(2)-transforms; Widder potential transforms; Glasser transforms; P(v,2)-transforms; Hankel transforms; K(v)-transforms; Parseval-Goldstein-type theorems; IDENTITIES; L-2-TRANSFORM