Inequalities for zeros of associated polynomials and derivatives of orthogonal polynomials

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dc.contributor.authorDimitrov, D. K.
dc.contributor.authorRonveaux, A.
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.contributor.institutionFac Univ Notre Dame Paix
dc.date.accessioned2014-05-20T14:01:35Z
dc.date.available2014-05-20T14:01:35Z
dc.date.issued2001-02-01
dc.description.abstractIt is well known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial p(n)(x) interlace with the zeros of p(n)(x) itself. The natural question of how these zeros interlace is under discussion. We give a sufficient condition for the mutual location of kth, 1 less than or equal to k less than or equal to n - 1, zeros of the associated polynomial and the derivative of an orthogonal polynomial in terms of inequalities for the corresponding Cotes numbers. Applications to the zeros of the associated polynomials and the derivatives of the classical orthogonal polynomials are provided. Various inequalities for zeros of higher order associated polynomials and higher order derivatives of orthogonal polynomials are proved. The results involve both classical and discrete orthogonal polynomials, where, in the discrete case, the differential operator is substituted by the difference operator. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.en
dc.description.affiliationUniv Estadual Paulista, IBILCE, Dept Ciências Computacao & Estatist, BR-15054000 Sao Jose do Rio Preto, SP, Brazil
dc.description.affiliationFac Univ Notre Dame Paix, B-5000 Namur, Belgium
dc.description.affiliationUnespUniv Estadual Paulista, IBILCE, Dept Ciências Computacao & Estatist, BR-15054000 Sao Jose do Rio Preto, SP, Brazil
dc.format.extent321-331
dc.identifierhttp://dx.doi.org/10.1016/S0168-9274(00)00013-1
dc.identifier.citationApplied Numerical Mathematics. Amsterdam: Elsevier B.V., v. 36, n. 2-3, p. 321-331, 2001.
dc.identifier.doi10.1016/S0168-9274(00)00013-1
dc.identifier.issn0168-9274
dc.identifier.lattes1681267716971253
dc.identifier.urihttp://hdl.handle.net/11449/21735
dc.identifier.wosWOS:000166460600012
dc.language.isoeng
dc.publisherElsevier B.V.
dc.relation.ispartofApplied Numerical Mathematics
dc.relation.ispartofjcr1.263
dc.relation.ispartofsjr0,930
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectclassical orthogonal polynomialspt
dc.subjectdiscrete orthogonal polynomialspt
dc.subjectassociated polynomialspt
dc.subjectinterlacingpt
dc.subjectCotes numberspt
dc.titleInequalities for zeros of associated polynomials and derivatives of orthogonal polynomialsen
dc.typeArtigo
dcterms.licensehttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dcterms.rightsHolderElsevier B.V.
unesp.author.lattes1681267716971253
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Biociências Letras e Ciências Exatas, São José do Rio Pretopt

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