Asymptotics for Orthogonal Polynomials with Respect to the Jacobi Measure Modified by a Rational Factor

摘要

Let μ be the Jacobi measure and let the rational function r(x) = uN(x)/vM(x), UN and vM monic polynomials of degree N and M respectively, be such that uN and vM have all zeros in R[-1, 1]. In this paper we study the asymptotic properties of the polynomials orthogonal with respect to the Jacobi measure modified by a rational factor r(x)idμ(x).