arXiv subjects

Ahmet Dernek

Publications and source records attributed to Ahmet Dernek.

2 recordsLinked to original sources

arXiv2008

Identities for the Hankel transform and their applications

In the present paper the authors show that iterations of the Hankel transform with $\mathscr{K}_ν$-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.

math.CA↗

arXiv2008

New identities for the Glasser transform and their applications

In the present paper the authors show that an iteration of the $\mathscr{L}_{2}$-transform by itself is a constant multiple of the Glasser transform. Using this iteration identity, a Parseval-Goldstein type theorem for $\mathscr{L}_{2}$-transform and the Glasser 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 as illustration of the results presented here.

math.CA↗