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American Mathematical Society, Mathematics of Computation, 278(81), p. 991-1004

DOI: 10.1090/s0025-5718-2011-02553-6

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INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

Journal article published in 2011 by Ivan Area ORCID, Dimitar Kolev Dimitrov ORCID, Eduardo Godoy, Fernando R. Rafaeli
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) ; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) ; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) ; Processo FAPESP: 09/13832-9 ; 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.