Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials

Martínez-Finkelshtein, Andrei; Moreno Balcázar, Juan José; Pijeira Cabrera, Héctor Esteban

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Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials

Author(s): Martínez-Finkelshtein, Andrei; Moreno Balcázar, Juan José; Pijeira Cabrera, Héctor Esteban

Publisher: Elsevier

Issued date: 1997-07-08

Citation: Journal of Computational and Applied Mathematics, 1997, vol. 81, n. 2, p. 211-216

ISSN: 0377-0427

DOI: 10.1016/S0377-0427(97)00059-9

Sponsor: Research by first (A.M.F.) and second (J.J.M.B.) was partially supported by Junta de Andalucía, Grupo de Investigación FQM 0229.

Review: PeerReviewed

Publisher version: http://dx.doi.org/10.1016/S0377-0427(97)00059-9

Keywords: Sobolev orthogonal polynomials , Asymptotics

URI: http://hdl.handle.net/10016/6572

Rights: © Elsevier

Abstract:

We study the asymptotic behaviour of the monic orthogonal polynomials with respect to the Gegenbauer-Sobolev inner product (f,g)_S= <f,g> + λ<f',g'> where <f,g> = \int_{-1}\sp 1f(x)g(x)(1-x\sp 2)\sp {\alpha-\frac{1}{2}}dx, with α > -1/2 and λ > 0. The asymptot [+]