We consider an equationHere α, β, γ are constants, moreover 0 < 2α, 2β, 2γ < 1. Main result of this paper is a construction of eight fundamental solutions for above-given equation in an explicit form. They are expressed by Lauricella's hypergeometric functions of three variables. Using expansion of Lauricella's hypergeometric function by products of Gauss's hypergeometric functions, it is proved that the found solutions have a singularity of the order 1/r at r → 0. Furthermore, some properties of these solutions, which will be used at solving boundary-value problems for afore-mentioned equation are shown.
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 .
In this paper, by using certain inverse pairs of symbolic operators introduced by Choi and Hasanov in 2011, we establish several decomposition formulas associated with the Gaussian triple hypergeometric functions. Some transformation formulas for these functions have also been obtained.
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