Certain case of the Riemann–Hilbert boundary value problem with peculiarities of coefficients

We consider the Riemann–Hilbert boundary value problem for a case where the coefficients have countable set of discontinuity points of the first kind such that the series of jumps of argument of the coefficient function is divergent, but the index of the Hilbert problem is finite. We derive the formulae for general solution of the problem and investigate the picture of solvability.