The new approach to solving the Riemann boundary value problem with infinite index

This research considers Riemann–Hilbert boundary value problem with infinite index where edge condition of problem is established by the real axis. To solve this problem the approach based on the removal of the infinite discontinuity of the argument of boundary condition coefficient is used. The approach is analogous to the one which, in the context of the finite index of the problem in researches by F. D. Gakhov, helps to remove a discontinuity of initial genre of boundary condition coefficient with specially created functions, different from the ones in this research.