Certain Integral Representations of Euler Type for the Exton Function X(2)

Exton [Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113-119] 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 Ψ2, a Humbert function Φ2. The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function X2 among his twenty Xi (i = 1, …, 20), whose kernels include the Exton function X2 itself, the Appell function F4, and the Lauricella function Fc.