The Laguerre-Sobolev-type orthogonal polynomials

被引：10
|
作者：
Duenas, Herbert [1 ,2 ]
Marcellan, Francisco [1 ]
机构：
[1] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain
[2] Univ Nacl Colombia, Dept Matemat, Bogota, Colombia
来源：
JOURNAL OF APPROXIMATION THEORY | 2010年 / 162卷 / 02期
关键词：
Quasi-orthogonal polynomials; Laguerre polynomials; Relative asymptotics; Mehler-Heine formula; Zeros;
D O I：
10.1016/j.jat.2009.07.006
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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 + N-p((j))(0)(q)((j))(0), where N is an element of R+ and j is an element of N. We Will focus Our attention on the outer relative asymptotics with respect to the standard Laguerre polynomials as well as oil all analog of the Mehler-Heine formula for the rescaled polynomials. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：421 / 440
页数：20
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