Some Parseval–Goldstein type identities involving the FS,2-transform, the FC,2-transform and the P4-transform and their applications

摘要

In the present paper the authors consider several new integral transforms including the FS,2-transform, the FC,2-transform and the P4-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.