Certain Integral Representations of Euler Type for the Exton Function X8

Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1, . . . , 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions 0F1, 1F1, a Humbert function Ψ1, and a Humbert function Φ2. The object of this paper is to present 18 new integral representations of Euler type for the Exton hypergeometric function X8, whose kernels include the Exton functions (X2, X8) itself, the Horn’s function H4, the Gauss hypergeometric function F , and Lauricella hypergeometric function FC . We also provide a system of partial differential equations satisfied by X8.