Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Zeros of Gegenbauer and Hermite polynomials and connection coefficients


Authors: Iván Area, Dimitar K. Dimitrov, Eduardo Godoy and André Ronveaux
Journal: Math. Comp. 73 (2004), 1937-1951
MSC (2000): Primary 33C45, 26C10
Published electronically: March 23, 2004
MathSciNet review: 2059744
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2000): 33C45, 26C10

Retrieve articles in all journals with MSC (2000): 33C45, 26C10


Additional Information

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: http://dx.doi.org/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
Published electronically: March 23, 2004
Article copyright: © Copyright 2004 American Mathematical Society