A new approach to solving homogeneous Riemann boundary-value problem on a ray with infinite index

We consider Riemann boundary-value problem with infinite index where the edge condition of a problem is given on positive real axis of a complex plane. To solve this problem we use an approach based on the removal of the infinite discontinuity of the argument of coefficient of boundary condition. The approach is analogous to that e one which, in the case of finite index of the problem in papers by F. D. Gakhov, helps to remove a discontinuity of coefficient of boundary condition with specially selected functions, different from the ones in this paper.