How to generate unknown orthogonal polynomials out of known orthogonal polynomials

We consider the problem of generating the three-term recursion coefficients of orthogonal polynomials for a weight function v(t)=r(t)w(t), obtained by modifying a given weight function w by a rational function. Algorithms for the construction of the orthogonal polynomials for the new weight v in terms of those for the old weight w are presented. All the methods are based on modified moments. As applications we present Gaussian quadrature rules for integrals in which the integrant has singularities close to the interval of integration, and the generation of orthogonal polynomials for the (finite) Hermite weight e^-t2, supported on a finite interval [-b, b].