On the uniform convergence of the approximate solution of singular integro-differential equation of the first kind

The article presents the study of the boundary problem for singular integro-differential equation of the first kind with Cauchy kernel. The authors introduce the pair of weight spaces to prove the correctness of the stated problem. The article states the sufficient conditions for the convergence of the general direct method, the method of orthogonal polynomials, and as a result uniform estimates for errors of approximate solution.