Asymptotic behaviour of Laguerre-Sobolev-type orthogonal polynomials. A nondiagonal case
[摘要] In this paper we study the asymptotic behaviour of polynomials orthogonal with respect to a Sobolev-type inner product < p, q >(s) =integral(infinity)(0) p(x)q(x)x(alpha)e(-x) dx + P(0)(t)AQ(0). alpha > -1, where p and q are polynomials with real coefficients, A = (M-0 lambda lambda M-1), P(0) = (p(0) p'(0)), Q(0) = (q(0) q'(0)), and A is a positive semidefinite matrix. We will focus our attention on their outer relative asymptotics with respect to the standard Laguerre polynomials as well as on an analog of the Mehler-Heine formula for the rescaled polynomials. (C) 2009 Elsevier B.V. All rights reserved.
[发布日期] 2010-12-15 [发布机构]
[效力级别] Proceedings Paper [学科分类]
[关键词] Quasi-orthogonal polynomials;Laguerre polynomials;Soholev-type inner products;Bessel function;Relative asymptotics;Outer relative asymptotics;Mehler-Heine formula [时效性]
