Identities for the Hankel transform and their applications

In the present paper the authors show that iterations of the Hankel transform with $\mathscr{K}_{\nu}$-transform is a constant multiple of the Widder transform. Using these iteration identities, several Parseval-Goldstein type theorems for these transforms are given. By making use of these results a number of new Goldstein type exchange identities are obtained for these and the Laplace transform. 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 illustration of the results presented here.Comment: 16 page

A Generalization of the Krätzel Function and Its Applications

In this paper, we introduce new functions Yρ,r(x) as a generalization of the Krätzel function. We investigate recurrence relations, Mellin transform, fractional derivatives, and integral of the function Yρ,r(x). We show that the function Yρ,r(x) is the solution of differential equations of fractional order