Asymptotics of Sobolev Orthogonal Polynomials for Coherent Pairs of Laguerre Type

Let ”Sn•n denote a sequence of polynomials orthogonal with respect to the Sobolev inner product f; g‘S D Z f x‘gx‘d 0x‘ C Z f 0x‘g0x‘d 1x‘; where > 0 and ”d 0; d 1• is a so-called coherent pair with at least one of the measures d 0 or d 1 a Laguerre measure. We investigate the asymptotic behaviour of Snx‘ outside the supports of d 0 and d 1, and n!C1. © 2000 Academic Press