INTEGRAL REPRESENTATIONS FOR SRIVASTAVA'S HYPERGEOMETRIC FUNCTION HB

Abstract

Abstract. While investigating the Lauricella’s list of 14 completesecond-order hypergeometric series in three variables, Srivastavanoticed the existence of three additional complete triple hypergeo-metric series of the second order, which were denoted by H A , H B and H C . Each of these three triple hypergeometric functions H A ,H B and H C has been investigated extensively in many di erentways including, for example, in the problem of nding their inte-gral representations of one kind or the other. Here, in this paper, weaim at presenting further integral representations for the Srivatava’striple hypergeometric function H A . 1. Introduction and PreliminariesIn the theory of hypergeometric functions of several variables, a re-markably large number of triple hypergeometric functions have beenintroduced and investigated. A comprehensive table of 205 distincttriple hypergeometric functions is provided in the work of Srivastavaand Karlsson [15, Chapter 3]. Out of these 205 distinct triple hyperge-ometric functions, Lauricella [8, p. 114] introduced fourteen completetriple hypergeometric functions of the second order. He denoted histriple hypergeometric functions by the symbols F