Quadrature Formulas for Singular Integrals Containing the Values of a Function and Its Derivatives

Quadrature formulas for singular integrals on the integration interval [−1, 1] with certain weight functions \(p(t)\) are constructed. The formulas use the values of the function and its derivatives at the zeros of the Chebyshev polynomial. The resulting formulas are quadrature formulas of the interpolation type and have an algebraic degree of accuracy \(2m - 1\) . The error estimate is given.