Mathematics of Computation

Author(s): Iván Area; Dimitar K. Dimitrov; Eduardo Godoy; André Ronveaux.
Journal: Math. Comp. 73 (2004), 1937-1951.
MSC (2000): Primary 33C45, 26C10
Posted: March 23, 2004
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Abstract: In this paper, sharp upper limit for the zeros of the ultraspherical polynomials are obtained via a result of Obrechkoff and certain explicit connection coefficients for these polynomials. As a consequence, sharp bounds for the zeros of the Hermite polynomials are obtained.

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Iván Area
Affiliation: Departamento de Matemática Aplicada II, E.T.S.E. Telecomunicación, Universidade de Vigo, Campus Lagoas--Marcosende, 36200 Vigo, Spain
Email: area@dma.uvigo.es

Dimitar K. Dimitrov
Affiliation: Departamento de Ciências de Computação e Estatística, IBILCE, Universidade Estadual Paulista, 15054-000 São José do Rio Preto, SP, Brazil
Email: dimitrov@dcce.ibilce.unesp.br

Eduardo Godoy
Affiliation: Departamento de Matemática Aplicada II, E.T.S.I. Industriales, Universidade de Vigo, Campus Lagoas--Marcosende, 36200 Vigo, Spain
Email: egodoy@dma.uvigo.es

André Ronveaux
Affiliation: Departement de Mathematique, Unité D'Analyse Mathématique et de Mécanique, Université Catholique de Louvain, Bâtiment Marc de Hemptinne, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium
Email: ronveaux@math.ucl.ac.be

DOI: 10.1090/S0025-5718-04-01642-4
PII: S 0025-5718(04)01642-4
Keywords: Orthogonal polynomials, zeros of Gegenbauer polynomials, zeros of Hermite polynomials, connection coefficients
Received by editor(s): October 14, 2002
Posted: March 23, 2004
Copyright of article: Copyright 2004, American Mathematical Society

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