Connection coefficients and zeros of orthogonal polynomials
Autor(a) principal: | |
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Data de Publicação: | 2001 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/S0377-0427(00)00653-1 http://hdl.handle.net/11449/21710 |
Resumo: | We discuss an old theorem of Obrechkoff and some of its applications. Some curious historical facts around this theorem are presented. We make an attempt to look at some known results on connection coefficients, zeros and Wronskians of orthogonal polynomials from the perspective of Obrechkoff's theorem. Necessary conditions for the positivity of the connection coefficients of two families of orthogonal polynomials are provided. Inequalities between the kth zero of an orthogonal polynomial p(n)(x) and the largest (smallest) zero of another orthogonal polynomial q(n)(x) are given in terms of the signs of the connection coefficients of the families {p(n)(x)} and {q(n)(x)}, An inequality between the largest zeros of the Jacobi polynomials P-n((a,b)) (x) and P-n((alpha,beta)) (x) is also established. (C) 2001 Elsevier B.V. B.V. All rights reserved. |
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Connection coefficients and zeros of orthogonal polynomialsconnection coefficientszeros of orthogonal polynomialsDescartes' rule of signsWronskiansinequalities for zerosWe discuss an old theorem of Obrechkoff and some of its applications. Some curious historical facts around this theorem are presented. We make an attempt to look at some known results on connection coefficients, zeros and Wronskians of orthogonal polynomials from the perspective of Obrechkoff's theorem. Necessary conditions for the positivity of the connection coefficients of two families of orthogonal polynomials are provided. Inequalities between the kth zero of an orthogonal polynomial p(n)(x) and the largest (smallest) zero of another orthogonal polynomial q(n)(x) are given in terms of the signs of the connection coefficients of the families {p(n)(x)} and {q(n)(x)}, An inequality between the largest zeros of the Jacobi polynomials P-n((a,b)) (x) and P-n((alpha,beta)) (x) is also established. (C) 2001 Elsevier B.V. B.V. All rights reserved.Univ Estadual Paulista, IBILCE, Dept Ciências Comp & Estatist, BR-15054000 Sao Jose do Rio Preto, SP, BrazilUniv Estadual Paulista, IBILCE, Dept Ciências Comp & Estatist, BR-15054000 Sao Jose do Rio Preto, SP, BrazilElsevier B.V.Universidade Estadual Paulista (Unesp)Dimitrov, D. K.2014-05-20T14:01:31Z2014-05-20T14:01:31Z2001-08-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article331-340application/pdfhttp://dx.doi.org/10.1016/S0377-0427(00)00653-1Journal of Computational and Applied Mathematics. Amsterdam: Elsevier B.V., v. 133, n. 1-2, p. 331-340, 2001.0377-0427http://hdl.handle.net/11449/2171010.1016/S0377-0427(00)00653-1WOS:000170613700027WOS000170613700027.pdf1681267716971253Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Computational and Applied Mathematics1.6320,938info:eu-repo/semantics/openAccess2024-01-05T06:28:39Zoai:repositorio.unesp.br:11449/21710Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:12:02.643638Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Connection coefficients and zeros of orthogonal polynomials |
title |
Connection coefficients and zeros of orthogonal polynomials |
spellingShingle |
Connection coefficients and zeros of orthogonal polynomials Dimitrov, D. K. connection coefficients zeros of orthogonal polynomials Descartes' rule of signs Wronskians inequalities for zeros |
title_short |
Connection coefficients and zeros of orthogonal polynomials |
title_full |
Connection coefficients and zeros of orthogonal polynomials |
title_fullStr |
Connection coefficients and zeros of orthogonal polynomials |
title_full_unstemmed |
Connection coefficients and zeros of orthogonal polynomials |
title_sort |
Connection coefficients and zeros of orthogonal polynomials |
author |
Dimitrov, D. K. |
author_facet |
Dimitrov, D. K. |
author_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Dimitrov, D. K. |
dc.subject.por.fl_str_mv |
connection coefficients zeros of orthogonal polynomials Descartes' rule of signs Wronskians inequalities for zeros |
topic |
connection coefficients zeros of orthogonal polynomials Descartes' rule of signs Wronskians inequalities for zeros |
description |
We discuss an old theorem of Obrechkoff and some of its applications. Some curious historical facts around this theorem are presented. We make an attempt to look at some known results on connection coefficients, zeros and Wronskians of orthogonal polynomials from the perspective of Obrechkoff's theorem. Necessary conditions for the positivity of the connection coefficients of two families of orthogonal polynomials are provided. Inequalities between the kth zero of an orthogonal polynomial p(n)(x) and the largest (smallest) zero of another orthogonal polynomial q(n)(x) are given in terms of the signs of the connection coefficients of the families {p(n)(x)} and {q(n)(x)}, An inequality between the largest zeros of the Jacobi polynomials P-n((a,b)) (x) and P-n((alpha,beta)) (x) is also established. (C) 2001 Elsevier B.V. B.V. All rights reserved. |
publishDate |
2001 |
dc.date.none.fl_str_mv |
2001-08-01 2014-05-20T14:01:31Z 2014-05-20T14:01:31Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1016/S0377-0427(00)00653-1 Journal of Computational and Applied Mathematics. Amsterdam: Elsevier B.V., v. 133, n. 1-2, p. 331-340, 2001. 0377-0427 http://hdl.handle.net/11449/21710 10.1016/S0377-0427(00)00653-1 WOS:000170613700027 WOS000170613700027.pdf 1681267716971253 |
url |
http://dx.doi.org/10.1016/S0377-0427(00)00653-1 http://hdl.handle.net/11449/21710 |
identifier_str_mv |
Journal of Computational and Applied Mathematics. Amsterdam: Elsevier B.V., v. 133, n. 1-2, p. 331-340, 2001. 0377-0427 10.1016/S0377-0427(00)00653-1 WOS:000170613700027 WOS000170613700027.pdf 1681267716971253 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Computational and Applied Mathematics 1.632 0,938 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
331-340 application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier B.V. |
publisher.none.fl_str_mv |
Elsevier B.V. |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129404330573824 |