Identities for the Hankel transform and their applications - DERNEK, AYŞE NEŞE (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2009)
In the present paper the authors show that iterations of the Hankel transform with Kv-transform is a constant multiple of the Widder transform. Using these iteration identities, several Parseval-Goldstein type theorems for these transforms are given. By making use of these results a number of new Goldstein type exchange identities are obtained for these and the Laplace transform. 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. (c) 2008 Elsevier Inc. All rights reserved.
Keywords: Widder transforms; Stieltjes transforms; Laplace transforms; Fourier sine transforms; Fourier cosine transforms; Hankel transforms; K-transforms; Mellin transforms; Goldstein type exchange identities; Parseval-Goldstein type theorems; THEOREM