  Recently found all the fundamental solutions of a multidimensional singular
elliptic equation are expressed in terms of the well-known Lauricella
hypergeometric function in many variables. In this paper, we find a unique
solution of the Dirichlet problem for an elliptic equation with several
singular coefficients in explicit form. When finding a solution, we use
decomposition formulas and some adjacent relations for the Lauricella
hypergeometric function in many variables.
