Application of Jacobi Polynomial and Multivariable Aleph- Function in Heat Conduction in Non-Homogeneous Moving Rectangular Parallelepiped

Abstract

The present paper deals with an application of Jacobi polynomial and multivariable Aleph-function to solve the differential equation of heat conduction in non-homogeneous moving rectangular parallelepiped. The temperature distribution in the parallelepiped, moving in a direction of the length (x-axis) between the limits x = −1 and x = 1 has been considered. The conductivity and the velocity have been assumed to be variables. We shall see two particular cases and the cases concerning Aleph-function of two variables and the I-function of two variables.

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]).…”