Approximate solution of hypersingular integral equations with Cauchy kernel

In the present paper, the hypersingular integral operator with Cauchy kernel H is approximated by a sequence of operators of the special form, it is proved that, the approximating operators Hn strongly converges to the operator H, for an algebraic polynomial of degree not higher than n, the operators Hn and H coincide, and is given a new method for the approximate solution of hypersingular integral equations with Cauchy kernel.