An integral associated with Aleph-functions of several variables

Abstract

The object of present document is to derive an integral pertaining to a products of two multivariable Aleph-functions, Two general class of polynomials and the M-serie with general arguments of quadratic nature. The result established in this paper are of general nature and hence encompass several particular cases.

Some Double Integrals Involving Multivariable I-Function

“…A similar argument given above will establish a large number of integral formulas whose integrand include diverse special functions such as the multivariable A-function (see [6]), the multivariable Aleph-function (see [1]), the Aleph-function of two variables (see [8]; see also [15]), the I-function of two variables (see [16]), the H-function of two variables (see [18]; see also [13]), the Aleph-function of one variable (see [21,22]), the I-function of one variable (see [14]), the A-function of one variable (see [5]).…”

“…. , z r ) = I 0,n 2 ;0,n 3 ;••• ;0,nr:m (1) ,n (1) ;••• ;m (r) ,n (r) p 2 ,q 2 ,p 3 ,q 3 ;••• ;pr,qr:p (1) ,q (1) ;••• ;p (r) ,q (r) (1)…”

“…In this paper, we aim to establish two double integral formulas involving the multivariable I-function (1). We also consider some special cases of the two integral formulas.…”

Unification of Ramanujan Integrals with Some Infinite Integrals and Multivariable Gimel-Function

“…5) If and , then the multivariable Gimel-function reduces in the multivariable Aleph-function defined by Ayant [2].…”

Double Fourier Cosine-Jacobi Series for Generalized Multivariable Gimel-Function

“…If and , then the generalized multivariable Gimel-function reduces in the generalized multivariable Aleph-function ( extension of multivariable Aleph-function defined by Ayant [1]).…”