Convexity of the extreme zeros of Gegenbauer and Laguerre polynomials

dc.contributor.authorDimitrov, D. K.
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2014-05-20T14:01:30Z
dc.date.available2014-05-20T14:01:30Z
dc.date.issued2003-04-01
dc.description.abstractLet C-n(lambda)(x), n = 0, 1,..., lambda > -1/2, be the ultraspherical (Gegenbauer) polynomials, orthogonal. in (-1, 1) with respect to the weight function (1 - x(2))(lambda-1/2). Denote by X-nk(lambda), k = 1,....,n, the zeros of C-n(lambda)(x) enumerated in decreasing order. In this short note, we prove that, for any n is an element of N, the product (lambda + 1)(3/2)x(n1)(lambda) is a convex function of lambda if lambda greater than or equal to 0. The result is applied to obtain some inequalities for the largest zeros of C-n(lambda)(x). If X-nk(alpha), k = 1,...,n, are the zeros of Laguerre polynomial L-n(alpha)(x), also enumerated in decreasing order, we prove that x(n1)(lambda)/(alpha + 1) is a convex function of alpha for alpha > - 1. (C) 2002 Published by Elsevier B.V. B.V.en
dc.description.affiliationUniv Estadual Paulista, IBILCE, Dept Ciências Comp & Estat, BR-15054000 Sao Jose do Rio Preto, SP, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, IBILCE, Dept Ciências Comp & Estat, BR-15054000 Sao Jose do Rio Preto, SP, Brazil
dc.format.extent171-180
dc.identifierhttp://dx.doi.org/10.1016/S0377-0427(02)00645-3
dc.identifier.citationJournal of Computational and Applied Mathematics. Amsterdam: Elsevier B.V., v. 153, n. 1-2, p. 171-180, 2003.
dc.identifier.doi10.1016/S0377-0427(02)00645-3
dc.identifier.fileWOS000181888700017.pdf
dc.identifier.issn0377-0427
dc.identifier.lattes1681267716971253
dc.identifier.urihttp://hdl.handle.net/11449/21697
dc.identifier.wosWOS:000181888700017
dc.language.isoeng
dc.publisherElsevier B.V.
dc.relation.ispartofJournal of Computational and Applied Mathematics
dc.relation.ispartofjcr1.632
dc.relation.ispartofsjr0,938
dc.rights.accessRightsAcesso aberto
dc.sourceWeb of Science
dc.subjectultraspherical polynomialspt
dc.subjectLaguerre polynomialspt
dc.subjectzerospt
dc.subjectconvexitypt
dc.subjectmonotonicitypt
dc.titleConvexity of the extreme zeros of Gegenbauer and Laguerre 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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