A Gauss quadrature formula for Cauchy type integrals (Q1120953)

The authors construct a Gauss quadrature formula for the numerical integration of Cauchy type integrals \[ I(f;\xi)=\int^{b}_{a}\frac{w(x)f(x)}{x-\xi}dx. \] For this, a set of orthogonal polynomials \(\{\phi_ n(x,\xi)\}\) with respect to w(x)/(x- \(\xi)\) is obtained where w(x) is a weight function. The derivation of the new formula follows the classical procedure. Numerical examples are considered.