A numerical method for the approximation of singular integrals of functions with a pole of order two (Q1339348)

The purpose of this paper is the derivation of approximate integration formulas for the integral \(I(\xi)= \int^ b_ a (f(x)/(x- \xi)^ 2)dx\), if the function \(f(x)\) is such that its fourth derivative \(f^{(IV)}(x)\) is continuous throughout the interval \((a,b)\). The main feature of the given method is that polynomial interpolation is carried out for the non-singular numerator rather than for the whole integrand function. The remainder terms of the presented numerical quadrature formulas are given.