Gauss quadrature rules for a generalized Hermite weight function

In this paper we give an algorithm for finding the coefficients in the three term recurrence relation for the polynomials orthogonal with respect to the weight function W(x) = ∣x − b∣2αexp[−(x + c)2] on RR, where α,b,c∈Rα,b,c∈R, 2α > −1. The algorithm is based on the discretization technique proposed by Gautschi, with the Lanczos algorithm. Using the coefficients obtained by this algorithm we construct the Gauss quadrature rules relative to the weight function W(x). To show the performance of the new algorithm we give some numerical examples.