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Zeros of classical orthogonal polynomials of a discrete variable


Authors: Iván Area, Dimitar K. Dimitrov, Eduardo Godoy and Vanessa G. Paschoa
Journal: Math. Comp. 82 (2013), 1069-1095
MSC (2010): Primary 33C45; Secondary 26C10
DOI: https://doi.org/10.1090/S0025-5718-2012-02646-9
Published electronically: November 16, 2012
MathSciNet review: 3008850
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Abstract: In this paper we obtain sharp bounds for the zeros of classical orthogonal polynomials of a discrete variable, considered as functions of a parameter, by using a theorem of A. Markov and the so-called Hellmann-Feynman theorem. Comparisons with previous results for zeros of Hahn, Meixner, Kravchuk and Charlier polynomials are also presented.


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Additional Information

Iván Area
Affiliation: Departamento de Matemática Aplicada II, E.E. Telecomunicación, Universidade de Vigo, Campus Lagoas-Marcosende, 36310 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@ibilce.unesp.br

Eduardo Godoy
Affiliation: Departamento de Matemática Aplicada II, E.E. Industrial, Universidade de Vigo, Campus Lagoas-Marcosende, 36310 Vigo, Spain
Email: egodoy@dma.uvigo.es

Vanessa G. Paschoa
Affiliation: Departamento de Matemática Aplicada, IMECC, Universidade Estadual de Campinas (UNICAMP), 13083-859 Campinas, SP, Brazil
Email: van{\textunderscore}gp@hotmail.com

DOI: https://doi.org/10.1090/S0025-5718-2012-02646-9
Keywords: Orthogonal polynomials of a discrete variable, Zeros, Charlier polynomials, Kravchuk polynomials, Meixner polynomials, Hahn polynomials, Gram polynomials
Received by editor(s): September 16, 2011
Published electronically: November 16, 2012
Additional Notes: This research was supported by the joint project CAPES(Brazil)/DGU(Spain), Grants 160/08 and PHB2007–0078, by the Brazilian foundations CNPq under Grant 305622/2009–9 and FAPESP under Grant 2009/13832–9 and by the Ministerio de Ciencia e Innovación of Spain under grant MTM2009–14668–C02–01, co-financed by the European Community fund FEDER
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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