Some identities for the Glasser transform and their applications

Authors: FARUK UÇAR

Abstract: In the present paper we consider a new integral transform, denoted by $\mathcal{G}_{\nu}$, which may be regarded as a generalization of the well-known transform due to Glasser. Many identities involving this transform 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.

Keywords: Laplace transforms, Widder potential transforms, Fourier sine transforms, Fourier cosine transforms, $\mathcal{H} _{\nu}$-transforms, $\mathcal{K}_{\nu}$-transforms, Parseval--Goldstein type theorems

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