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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Inequalities for zeros of Jacobi polynomials via Obrechkoff's theorem


Authors: Iván Area, Dimitar K. Dimitrov, Eduardo Godoy and Fernando R. Rafaeli
Journal: Math. Comp. 81 (2012), 991-1004
MSC (2010): Primary 33C45, 26C10
Published electronically: November 14, 2011
MathSciNet review: 2869046
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Abstract: In this paper we obtain sharp limits for all the zeros of Jacobi polynomials. We employ Obrechkoff's theorem on generalized Descartes' rule of signs and certain elaborated connection formulae which involve Jacobi and Laguerre polynomials.


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Additional Information

Iván Area
Affiliation: Departamento de Matemática Aplicada II, E.T.S.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 (UNESP), 15054-000 São José do Rio Preto, SP, Brazil
Email: dimitrov@ibilce.unesp.br

Eduardo Godoy
Affiliation: Departamento de Matemática Aplicada II, E.T.S.I. Industriales, Universidade de Vigo, Campus Lagoas–Marcosende, 36310 Vigo, Spain.
Email: egodoy@dma.uvigo.es

Fernando R. Rafaeli
Affiliation: Departamento de Matemática, Estatística e Computação, FCT, Universidade Estadual Paulista (UNESP), 19060-900 Presidente Prudente, SP, Brazil
Email: rafaeli@fct.unesp.br

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02553-6
PII: S 0025-5718(2011)02553-6
Keywords: Connection formula, Obrechkoff’s theorem, zeros, Jacobi polynomial, Laguerre polynomial.
Received by editor(s): February 21, 2011
Published electronically: November 14, 2011
Additional Notes: Research 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 MCT of Spain under grant MTM2009-14668-C02-01, co-financed by the European Community fund FEDER
Article copyright: © Copyright 2011 American Mathematical Society