A quadrature rule of interpolatory type for Cauchy integrals

We construct a quadrature rule of interpolatory-type based on a trigonometric interpolation for Cauchy integrals. We obtain the same error bound O(|aNN|) as Hasegawa and Torii (Math. Comp. 56 (1991) 741–754). Numerical examples are included to substantiate the performance of the present method.