Inequalities for zeros of Jacobi polynomials via Obrechkoff’s theorem
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- by Iván Area, Dimitar K. Dimitrov, Eduardo Godoy and Fernando R. Rafaeli PDF
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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.References
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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
- MR Author ID: 308699
- 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
- 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
- © Copyright 2011 American Mathematical Society
- Journal: Math. Comp. 81 (2012), 991-1004
- MSC (2010): Primary 33C45, 26C10
- DOI: https://doi.org/10.1090/S0025-5718-2011-02553-6
- MathSciNet review: 2869046