Some Parseval-Goldstein type identities involving the F-S,F-2-transform, the F-C,F-2-transform and the P-4-transform and their applications

Abstract

In the present paper the authors consider several new integral transforms including the F-S,F-2-transform, the F-C,F-2-transform and the P-4-transform as generalizations of the classical Fourier sine transform, the classical Fourier cosine transform, and the classical Stieltjes transform, respectively. 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 illustrations of the results presented here. (C) 2008 Elsevier Inc. All rights reserved.