Abstract

In this paper, we first evaluate a unified and general finite multiple integral whose integrand involves the product of the functions and the multivariable Gimel-function occurring in the integrand involve the product of factors of the form , while that of occurring herein involves a finite series of such factors. On account of the most general nature of the functions occurring in the integrand of our main integral, a large number of new and known integrals can easily be obtained from ot merely by specializing the functions and parameters involved therein. At the end of this study, we illustrate a new integral whose integrand involves a product of the Jacobi polynomial, the Appell’s function and the Bessel function