Hilbert boundary-value problem with different two-sided power-law vorticity at infinity

We consider the Hilbert boundary-value problem for the half-plane with the countable set of points of discontinuity of the first kind and unique point of discontinuity of the second kind at infinity of the argument of function of coefficients of the boundary condition. This leads to the different two-sided power-law vorticity at infinity. In this paper we derive the general solution and deduce the full solution to the homogeneous problem for the special class of function. We also found the the general solution of the non-homogeneous problem.