Inequalities for zeros of Jacobi polynomials via Sturm's theorem: Gautschi's conjectures

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dc.contributor.authorLun, Yen Chi
dc.contributor.authorRafaeli, Fernando Rodrigo [UNESP]
dc.contributor.institutionUniversidade Estadual de Campinas (UNICAMP)
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2015-03-18T15:56:41Z
dc.date.available2015-03-18T15:56:41Z
dc.date.issued2014-11-01
dc.description.abstractLet x(n,k)((alpha,beta)), k = 1, ... , n, be the zeros of Jacobi polynomials P-n((alpha,beta)) (x) arranged in decreasing order on (-1, 1), where alpha, beta > -1, and theta((alpha,beta))(n,k) = arccos x(n,k)((alpha,beta)). Gautschi, in a series of recent papers, conjectured that the inequalitiesn theta((alpha,beta))(n,k) < (n + 1)theta((alpha,beta))(n+1,k)and(n + (alpha + beta + 3)/2)theta((alpha,beta))(n+1,k) < (n + (alpha + beta + 1)/2)theta((alpha,beta))(n,k),hold for all n >= 1, k = 1, ... , n, and certain values of the parameters alpha and beta. We establish these conjectures for large domains of the (alpha, beta)-plane by using a Sturmian approach.en
dc.description.affiliationUniv Estadual Campinas UNICAMP, Sao Paulo, Brazil
dc.description.affiliationUniv Estadual Paulista UNESP, Sao Paulo, Brazil
dc.description.affiliationUnespUniv Estadual Paulista UNESP, Sao Paulo, Brazil
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.format.extent549-563
dc.identifierhttp://link.springer.com/article/10.1007%2Fs11075-013-9807-7
dc.identifier.citationNumerical Algorithms. Dordrecht: Springer, v. 67, n. 3, p. 549-563, 2014.
dc.identifier.doi10.1007/s11075-013-9807-7
dc.identifier.issn1017-1398
dc.identifier.urihttp://hdl.handle.net/11449/117661
dc.identifier.wosWOS:000344598600005
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofNumerical Algorithms
dc.relation.ispartofjcr1.536
dc.relation.ispartofsjr0,981
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectGautschi's conjecturesen
dc.subjectJacobi polynomialsen
dc.subjectZerosen
dc.subjectInequalitiesen
dc.titleInequalities for zeros of Jacobi polynomials via Sturm's theorem: Gautschi's conjecturesen
dc.typeArtigo
dcterms.licensehttp://www.springer.com/open+access/authors+rights?SGWID=0-176704-12-683201-0
dcterms.rightsHolderSpringer
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Biociências Letras e Ciências Exatas, São José do Rio Pretopt

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