  The second Stokes problem with specular - diffusive boundary conditions of
the kinetic theory is considered. The new method of the decision of the
boundary problems of the kinetic theory is applied. The method allows to
receive the decision with any degree of accuracy. At the basis of a method lays
the idea of representation of a boundary condition on distribution function in
the form of a source in the kinetic equation. By means of integrals Fourier the
kinetic equation with a source is reduced to the integral equation of Fredholm
type of the second kind. The decision is received in the form of Neumann's
series.
