While investigating the Lauricella's list of 14 complete secondorder hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric 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 different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for each of Srivastava's triple hypergeometric functions H A , H B and H C .

With the help of some techniques based upon certain inverse pairs of symbolic operators, the authors investigate several decomposition formulas associated with Srivastava's hypergeometric functions H A , H B and H C in three variables. Many operator identities involving these pairs of symbolic operators are first constructed for this purpose. By means of these operator identities, as many as 15 decomposition formulas are then found, which express the aforementioned triple hypergeometric functions in terms of such simpler functions as the products of the Gauss and Appell hypergeometric functions. Other closely-related results are also considered briefly.

Abstract. While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by HA, HB and HC . Each of these three triple hypergeometric functions HA, HB and HC has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function HC .

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Exton introduced 20 distinct triple hypergeometric functions whose names are X i (i = 1,. .. , 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions 0 F 1 , 1 F 1 , a Humbert function Ψ 2 , a Humbert function Φ 2. The object of this paper is to present 25 (presumably new) integral representations of Euler types for the Exton hypergeometric function X 5 among his twenty X i (i = 1,. .. , 20), whose kernels include the Exton function X5 itself, the Exton function X 6 , the Horn's functions H 3 and H 4 , and the hypergeometric function F = 2 F 1 .