Spatial boundary problem with the Dirichlet–Neumann condition for a singular elliptic equation

In the present work we find an explicit solution of a boundary problem with the Dirichlet–Neumann condition for elliptic equation with singular coefficients in a quarter of ball. For this aim the method of Green’s function has been used. Since, found Green’s function contains a hypergeometric function of Appell, we had to deal with decomposition formulas, formulas of differentiation and some adjacent relations for this hypergeometric function in order to get explicit solution of the formulated problem.