Linearly Independent Solutions and Integral Representations for Certain Quadruple Hypergeometric Function

Abstract

Recently, hypergeometric functions of four variables are investigated by Bin-Saad and Younis. In this manuscript, our goal is to initiate a new quadruple hypergeometric function denoted by X844, and then, we ensure the existence of solutions of systems of partial differential equations for this function. We also establish some integral representations involving the quadruple hypergeometric function X844.