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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
Posted:
November 14, 2011
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Additional Information
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
Posted:
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
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