Fundamental solutions for a class of three-dimensional elliptic equations with singular coefficients

in a domain R+3 ≡ {(x, y, z) : x > 0, y > 0, z > 0}. Here 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.