Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article; Proceedings Paper

Bracciali, Cleonice F.¹  Castano-Garcia, Laura²  Moreno-Balcazar, Juan J.² 

[1] UNESP Univ Estadual Paulista, DCCE, IBILCE, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil

[2] Univ Almeria, Dpto Estadist & Matemat Aplicada, Almeria 04120, Spain

关键词: Sobolev orthogonal polynomials;    Asymptotics;    Mehler-Heine type formulas;   

DOI  :  10.1016/j.cam.2010.05.028

来源: Elsevier

【 摘 要 】

We consider the Sobolev inner product < f.g > = integral(1)(-1) f(x)g(x)(1 - x(2))(alpha-1/2) dx + integral f'(x)g'(x)d psi(x), alpha > -1/2, where d(psi) is a measure involving a Gegenbauer weight and with mass points outside the interval (-1, 1). We study the asymptotic behaviour of the polynomials which are orthogonal with respect to this inner product. We obtain the asymptotics of the largest zeros of these polynomials via a Mehler-Heine type formula. These results are illustrated with some numerical experiments. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free