The Laguerre-Sobolev-type orthogonal polynomials

JOURNAL OF APPROXIMATION THEORY

卷:162

Article

Duenas, Herbert^1,2  Marcellan, Francisco¹ 

[1] Univ Carlos III Madrid, Dept Matemat, Leganes 28911, Spain

[2] Univ Nacl Colombia, Dept Matemat, Bogota, Colombia

关键词: Quasi-orthogonal polynomials;    Laguerre polynomials;    Relative asymptotics;    Mehler-Heine formula;    Zeros;   

DOI  :  10.1016/j.jat.2009.07.006

来源: Elsevier

【 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.

【 授权许可】

Free