Monotonicity of zeros of Jacobi polynomials
Autor(a) principal: | |
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Data de Publicação: | 2007 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.jat.2007.04.004 http://hdl.handle.net/11449/21723 |
Resumo: | Denote by x(nk)(alpha, beta), k = 1...., n, the zeros of the Jacobi polynornial P-n((alpha,beta)) (x). It is well known that x(nk)(alpha, beta) are increasing functions of beta and decreasing functions of alpha. In this paper we investigate the question of how fast the functions 1 - x(nk)(alpha, beta) decrease as beta increases. We prove that the products t(nk)(alpha, beta) := f(n)(alpha, beta) (1 - x(nk)(alpha, beta), where f(n)(alpha, beta) = 2n(2) + 2n(alpha + beta + 1) + (alpha + 1)(beta + 1) are already increasing functions of beta and that, for any fixed alpha > - 1, f(n)(alpha, beta) is the asymptotically extremal, with respect to n, function of beta that forces the products t(nk)(alpha, beta) to increase. (c) 2007 Elsevier B.V. All rights reserved. |
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Repositório Institucional da UNESP |
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Monotonicity of zeros of Jacobi polynomialszerosJacobi polynomialsmonotonicityDenote by x(nk)(alpha, beta), k = 1...., n, the zeros of the Jacobi polynornial P-n((alpha,beta)) (x). It is well known that x(nk)(alpha, beta) are increasing functions of beta and decreasing functions of alpha. In this paper we investigate the question of how fast the functions 1 - x(nk)(alpha, beta) decrease as beta increases. We prove that the products t(nk)(alpha, beta) := f(n)(alpha, beta) (1 - x(nk)(alpha, beta), where f(n)(alpha, beta) = 2n(2) + 2n(alpha + beta + 1) + (alpha + 1)(beta + 1) are already increasing functions of beta and that, for any fixed alpha > - 1, f(n)(alpha, beta) is the asymptotically extremal, with respect to n, function of beta that forces the products t(nk)(alpha, beta) to increase. (c) 2007 Elsevier B.V. All rights reserved.Univ Estadual Paulista, Dept Ciências Computacao & Estat, IBILCE, São Paulo, BrazilUniv Estadual Paulista, Dept Ciências Computacao & Estat, IBILCE, São Paulo, BrazilElsevier B.V.Universidade Estadual Paulista (Unesp)Dimitrov, Dimitar K. [UNESP]Rafaeli, Fernando R. [UNESP]2014-05-20T14:01:33Z2014-05-20T14:01:33Z2007-11-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article15-29application/pdfhttp://dx.doi.org/10.1016/j.jat.2007.04.004Journal of Approximation Theory. San Diego: Academic Press Inc. Elsevier B.V., v. 149, n. 1, p. 15-29, 2007.0021-9045http://hdl.handle.net/11449/2172310.1016/j.jat.2007.04.004WOS:000251646600002WOS000251646600002.pdfWeb of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Approximation Theory0.9390,907info:eu-repo/semantics/openAccess2023-10-24T06:06:26Zoai:repositorio.unesp.br:11449/21723Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-10-24T06:06:26Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Monotonicity of zeros of Jacobi polynomials |
title |
Monotonicity of zeros of Jacobi polynomials |
spellingShingle |
Monotonicity of zeros of Jacobi polynomials Dimitrov, Dimitar K. [UNESP] zeros Jacobi polynomials monotonicity |
title_short |
Monotonicity of zeros of Jacobi polynomials |
title_full |
Monotonicity of zeros of Jacobi polynomials |
title_fullStr |
Monotonicity of zeros of Jacobi polynomials |
title_full_unstemmed |
Monotonicity of zeros of Jacobi polynomials |
title_sort |
Monotonicity of zeros of Jacobi polynomials |
author |
Dimitrov, Dimitar K. [UNESP] |
author_facet |
Dimitrov, Dimitar K. [UNESP] Rafaeli, Fernando R. [UNESP] |
author_role |
author |
author2 |
Rafaeli, Fernando R. [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Dimitrov, Dimitar K. [UNESP] Rafaeli, Fernando R. [UNESP] |
dc.subject.por.fl_str_mv |
zeros Jacobi polynomials monotonicity |
topic |
zeros Jacobi polynomials monotonicity |
description |
Denote by x(nk)(alpha, beta), k = 1...., n, the zeros of the Jacobi polynornial P-n((alpha,beta)) (x). It is well known that x(nk)(alpha, beta) are increasing functions of beta and decreasing functions of alpha. In this paper we investigate the question of how fast the functions 1 - x(nk)(alpha, beta) decrease as beta increases. We prove that the products t(nk)(alpha, beta) := f(n)(alpha, beta) (1 - x(nk)(alpha, beta), where f(n)(alpha, beta) = 2n(2) + 2n(alpha + beta + 1) + (alpha + 1)(beta + 1) are already increasing functions of beta and that, for any fixed alpha > - 1, f(n)(alpha, beta) is the asymptotically extremal, with respect to n, function of beta that forces the products t(nk)(alpha, beta) to increase. (c) 2007 Elsevier B.V. All rights reserved. |
publishDate |
2007 |
dc.date.none.fl_str_mv |
2007-11-01 2014-05-20T14:01:33Z 2014-05-20T14:01:33Z |
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/j.jat.2007.04.004 Journal of Approximation Theory. San Diego: Academic Press Inc. Elsevier B.V., v. 149, n. 1, p. 15-29, 2007. 0021-9045 http://hdl.handle.net/11449/21723 10.1016/j.jat.2007.04.004 WOS:000251646600002 WOS000251646600002.pdf |
url |
http://dx.doi.org/10.1016/j.jat.2007.04.004 http://hdl.handle.net/11449/21723 |
identifier_str_mv |
Journal of Approximation Theory. San Diego: Academic Press Inc. Elsevier B.V., v. 149, n. 1, p. 15-29, 2007. 0021-9045 10.1016/j.jat.2007.04.004 WOS:000251646600002 WOS000251646600002.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Journal of Approximation Theory 0.939 0,907 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
15-29 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_ |
1803046132352286720 |