Ser. Mat. 13 (2003), 49–63. NUMERICAL CONSTRUCTION OF THE GENERALIZED HERMITE POLYNOMIALS

In this paper we are concerned with polynomials orthogonal with respect to the generalized Hermite weight function w(x) = |x − z|γ exp(−x2) on R, where z ∈ R and γ> −1. We give a numerically stable method for finding re-cursion coefficients in the three term recurrence relation for such orthogonal polynomials, using some nonlinear recurrence relations, asymptotic expan-sions, as well as the discretized Stieltjes-Gautschi procedure. 1