New Identities on Some Generalized Integral Transforms and Their Applications

Abstract

In this paper, the authors give an iteration identity for the generalized Laplace transform L2n and the generalized Glasser transform G2n. Using this identity, a Parseval-Goldstein type theorem for the L2n-transform and the G2n-transform is given. By making use of these results, 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.