Convexity of the extreme zeros of Gegenbauer and Laguerre polynomials
dc.contributor.author | Dimitrov, D. K. | |
dc.contributor.institution | Universidade Estadual Paulista (Unesp) | |
dc.date.accessioned | 2014-05-20T14:01:30Z | |
dc.date.available | 2014-05-20T14:01:30Z | |
dc.date.issued | 2003-04-01 | |
dc.description.abstract | Let 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.affiliation | Univ Estadual Paulista, IBILCE, Dept Ciências Comp & Estat, BR-15054000 Sao Jose do Rio Preto, SP, Brazil | |
dc.description.affiliationUnesp | Univ Estadual Paulista, IBILCE, Dept Ciências Comp & Estat, BR-15054000 Sao Jose do Rio Preto, SP, Brazil | |
dc.format.extent | 171-180 | |
dc.identifier | http://dx.doi.org/10.1016/S0377-0427(02)00645-3 | |
dc.identifier.citation | Journal of Computational and Applied Mathematics. Amsterdam: Elsevier B.V., v. 153, n. 1-2, p. 171-180, 2003. | |
dc.identifier.doi | 10.1016/S0377-0427(02)00645-3 | |
dc.identifier.file | WOS000181888700017.pdf | |
dc.identifier.issn | 0377-0427 | |
dc.identifier.lattes | 1681267716971253 | |
dc.identifier.uri | http://hdl.handle.net/11449/21697 | |
dc.identifier.wos | WOS:000181888700017 | |
dc.language.iso | eng | |
dc.publisher | Elsevier B.V. | |
dc.relation.ispartof | Journal of Computational and Applied Mathematics | |
dc.relation.ispartofjcr | 1.632 | |
dc.relation.ispartofsjr | 0,938 | |
dc.rights.accessRights | Acesso aberto | |
dc.source | Web of Science | |
dc.subject | ultraspherical polynomials | pt |
dc.subject | Laguerre polynomials | pt |
dc.subject | zeros | pt |
dc.subject | convexity | pt |
dc.subject | monotonicity | pt |
dc.title | Convexity of the extreme zeros of Gegenbauer and Laguerre polynomials | en |
dc.type | Artigo | |
dcterms.license | http://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy | |
dcterms.rightsHolder | Elsevier B.V. | |
unesp.author.lattes | 1681267716971253 | |
unesp.campus | Universidade Estadual Paulista (Unesp), Instituto de Biociências Letras e Ciências Exatas, São José do Rio Preto | pt |
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