Approximate solution of an integral equation of the first kind with the multiplicative kernel of Cauchy by method of orthogonal polynomials

Numerical methods for solving singular integral equation of the first kind with a special form of the right-hand side are developed. The proposed schemes are based on the decomposition of the singular integrals with power-logarithmic singularity in Chebyshev polynomials of the first and second kind. Accuracy estimates of the considered methods are presented.