Asymptotics of recurrence coefficients for orthonormal polynomials on the line—Magnus’s method revisited

Abstract

We use Freud equations to obtain the main term in the asymptotic expansion of the recurrence coefficients associated with orthonormal polynomials pn(w2) for weights w = W exp(-Q) on the real line where Q is an even polynomial of fixed degree with nonnegative coefficients or where Q(x) -- exp(x2m), m ≥ 1. Here W(x) = |x|ρ for some real ρ > -1.