The escape function u(μ) (i.e., the boundary solution of the Milne problem for a semi-infinite atmosphere) is considered. It is presented in the form u(μ) = u₀(μ) + √(1 — λ)u₁(μ) + (1 — λ)u₂(μ) + ..., where λ is the single-scattering albedo. A rather accurate approximate formula for a the function u₀(μ) is obtained for not highly elongated phase function. An approximate expression for the function u₂(μ) is also derived, it is exact in the case of the most simple anisotropic scattering.