Asymptotic behaviour of Laguerre-Sobolev-type orthogonal polynomials. A nondiagonal case

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article; Proceedings Paper

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;    Soholev-type inner products;    Bessel function;    Relative asymptotics;    Outer relative asymptotics;    Mehler-Heine formula;   

DOI  :  10.1016/j.cam.2009.07.055

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 + 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.

【 授权许可】

Free