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Abstract: In the present paper the authors consider the $\mathcal{P} { u,2}$-transformas a generalization of the Widder potential transform and the Glassertransform. The $\mathcal{P} { u,2}$-transform is obtained as an iteration ofthe the $\mathcal{L} {2}$-transform with itself. Many identities involvingthese transforms are given. By making use of these identities, a number of newParseval-Goldstein type identities are obtained for these and many otherwell-known integral transforms. The identities proven in this paper are shownto give rise to useful corollaries for evaluating infinite integrals of specialfunctions. Some examples are also given as illustration of the resultspresented here.



Author: Nese Dernek, Veli Kurt, Yilmaz Simsek, Osman Yurekli

Source: https://arxiv.org/



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