Abstract

In the present paper we consider a unied integral transform "Ultra Gamma Transform" (UGT) and its relation with fractional integral operators. We list out certain properties of this transform and present a table of UGT of elementary functions including trigonometric function as well as hyperbolic function in terms of generalized three parameter gamma function renamed as "Ultra Gamma Function" (UGF). We also point out certain special cases of this integral transform in terms of well-known classical integral transforms, other integral transforms and generalized gamma function that occurs in the study of scattering of waves and that with the classical gamma function in support of justication of the ndings. Finally some statistical aliations of UGF are reported from real life applications point of view.

Keywords and Phrases

Gamma Functions, Integral Transform, Fractional Integral Operators, Probability Distribution.

A.M.S. subject classification

Primary: 33B15, 44A30; Secondary: 26A33, 33B20, 44A10, 60E05, 74J20.

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