Laguerre-Sobolev orthogonal polynomials:: asymptotics for coherent pairs of type II

Let S-n be polynomials orthogonal with respect to the inner product (f,g)(s) = integral(0)(infinity) fgdmu(0) + lambda integral(0)(infinity) f'g'dmu(1), where dmu(0) = x(alpha)e(-x) dx, dmu(1) = x(alpha+1)e(-x)/x-xi dx + Mdelta(xi) with alpha > - 1, xi less than or equal to 0, M greater than or equal to 0, and lambda > 0. A strong asymptotic on (0, infinity), a Mehler-Heine type formula, a Plancherel-Rotach type exterior asymptotic as well as an upper estimate for S-n are obtained. As a consequence, we give asymptotic results for the zeros and critical points of S-n and the distribution of contracted zeros. Some numerical examples are shown. (C) 2003 Elsevier Science (USA). All rights reserved.