Certain Finite Integrals Related to the Products of Special Functions

Abstract

The aim of this paper is to establish a theorem associated with the product of the Aleph-function, the multivariable Aleph-function, and the general class of polynomials. The results of this theorem are unified in nature and provide a very large number of analogous results (new or known) involving simpler special functions and polynomials (of one or several variables) as special cases. The derived results lead to significant applications in physics and engineering sciences.

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

“…The Aleph-function of several variables generalizes the multivariable I-function defined by Sharma and Ahmad [26], which is a generalization of G and H-functions [8,21] of multiple variables. The multiple Mellin-Barnes integral occurring in this paper will be referred to as the multivariable Aleph-function throughout our present study and will be defined and represented as follows (see also, [4,[15][16][17]19]).…”