A Gauss quadrature rule for hypersingular integrals

We construct a set of polynomials Φn(x, t) which are orthogonal with respect to v(x, t) = w(x)/(x − t)p, t ∈ (a, b), where w(x) is a weight function and p is an integer. As an application these polynomials can be used to extract Gaussian quadrature rules for hypersingular integrals.