Certain finite double integrals involving the hypergeometric function and Aleph-function

Abstract

The aim of this document is to evaluate four finite double integrals involving the product of two hypergeometric functions and the Alephfunction. At the end of this paper , we evaluate few particular cases.

Integral Involving the Product of Multivariable Alephfunction, General Class of Srivastava Polynomials and Alephfunction of One Variable

“…The Aleph (ℵ)-function was established by Südland et al [30], but its notation and complete definition are offered below in terms of the Mellin-Barnes type integral (see also, [2,3,7,13,23,25]):…”

Fractional calculus pertaining to multivariable Aleph-function

“…The Aleph-function, introduced by Südland et al [30], however the notation and complete definition is presented here in the following manner in terms of the Mellin-Barnes type integral (see also, [1,2,11,15,26]): for all z different to 0 and…”

Integral Involving Aleph-Function and the Generalized Incomplete Hypergeometric Function

“…From the point of view of the applied scientists and engineers dealing with the practical application of differential equations, the role of special functions as an important tool of mathematical analysis. The ℵ-function was introduced by Südland et al [1,2], however the notation and complete definition is presented here in the following manner in terms of the Mellin-Barnes type integral (see also, [3,4,5,6,7,8,9,10]):…”