Otro
Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights
Registro en:
Journal of Computational and Applied Mathematics. Amsterdam: Elsevier B.V., v. 235, n. 4, p. 904-915, 2010.
0377-0427
10.1016/j.cam.2010.05.028
WOS:000283902100004
Autor
Bracciali, Cleonice Fátima
Castano-Garcia, Laura
Moreno-Balcazar, Juan J.
Resumen
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. Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)