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In this paper the method of spherical harmonics (MSH) is investigated, which is one of effective methods of approximative solution of the transport equation. On a unified methodical basis, boundary conditions on the outside and inner boundaries for every $P_N$-approximation of MSH are formulated. These boundary conditions coincide with Vladimirov’s conditions (for $N=2r+1$) and Rumjancev’s conditions (for every $N$). Symmetrization of the system of stationary equations of MSH for every $P_N$-approximation with arbitrary...