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 (i = 1, ..., 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions , , a Humbert function , a Humbert function . The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function among his twenty (i = 1, ..., 20), whose kernels include the Exton function itself, the Appell function , and the Lauricella function .