  The present work devoted to the finding 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 have 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.
