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.

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Srivastava and Panda have studied the simple and multiple generating relations concerning the multivariable H-function. The aim of this paper is to derive the various classes of simple and multiple generating relations involving the multivariable Aleph-function. The generating function is used in the theory of numbers, in physics and other fields of mathematics. We see the particular cases concerning the multivariable I-function, the Aleph-function of two variables and the I-function of two variables.

Recently Yashwant Singh et al [7] have studied Fourier series involving the I-function defined by V.P. Saxena [6]. Motivated by this work, we make an application of an integral involving sine function, exponential function, the product of Aleph-function of one variable and Kampé de Fériet's function. We also evaluate a multiple integral involving the Aleph-function to make its application to derive a multiple exponential Fourier series. Several particular cases are also given at the end.

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.