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The present work devoted to the finding explicit solution of a boundaryproblem with the Dirichlet-Neumann condition for elliptic equation withsingular coefficients in a quarter of ball. For this aim the method of Green'sfunction have been used. Since, found Green's function contains ahypergeometric function of Appell, we had to deal with decomposition formulas,formulas of differentiation and some adjacent relations for this hypergeometricfunction in order to get explicit solution of the formulated problem.

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