  We consider an equation $$ L_{\alpha ,\beta ,\gamma} (u) \equiv u_{xx} +
u_{yy} + u_{zz} + \displaystyle \frac{{2\alpha}}{x}u_x + \displaystyle
\frac{{2\beta}}{y}u_y + \displaystyle \frac{{2\gamma}}{z}u_z = 0 $$ in a domain
${\bf R}_3^ + \equiv {{({x,y,z}): x > 0, y > 0, z > 0}}$. Here $\alpha ,\beta
,\gamma$ are constants, moreover $0 < 2\alpha, 2\beta, 2\gamma < 1$. 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 with 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 $r \to
0$.
