Linearly independent solutions and integral representations for certain quadruple hypergeometric function (Q1981847)

Summary: 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 \(X_{84}^{(4)}\), 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 \(X_{84}^{(4)}\).