Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients
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Data de Publicação: | 2016 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1080/10652469.2016.1249866 http://hdl.handle.net/11449/162190 |
Resumo: | Consider the linear second-order differential equation An(z) y+ B-n(z) y' + C(n)y = 0, where A(n)(z) = a(2), nz(2) + a(1,n)z + a(0), n with a(2), n = 0, a2 1, n - 4a2, na0, n = 0,. n. N or a2, n = 0, a1, n = 0,. n. N, Bn(z) = b1, n + b0, nz are polynomials with complex coefficients and Cn. C. Under some assumptions over a certain class of lowering and raising operators, we show that for a sequence of polynomials (fn)8 n = 0 orthogonal on the unit circle to satisfy the differential equation (1.1), the polynomial fn must be of a specific form involving and extension of the Gauss and confluent hypergeometric series. |
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Repositório Institucional da UNESP |
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Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficientsOrthogonal polynomials on the unit circledifferential equationsspecial functionscomplex analysisConsider the linear second-order differential equation An(z) y+ B-n(z) y' + C(n)y = 0, where A(n)(z) = a(2), nz(2) + a(1,n)z + a(0), n with a(2), n = 0, a2 1, n - 4a2, na0, n = 0,. n. N or a2, n = 0, a1, n = 0,. n. N, Bn(z) = b1, n + b0, nz are polynomials with complex coefficients and Cn. C. Under some assumptions over a certain class of lowering and raising operators, we show that for a sequence of polynomials (fn)8 n = 0 orthogonal on the unit circle to satisfy the differential equation (1.1), the polynomial fn must be of a specific form involving and extension of the Gauss and confluent hypergeometric series.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Univ Fed Rio de Janeiro, Dept Matemat, Rio De Janeiro, BrazilUniv Estadual Paulista, Dept Matemat Aplicada, Campus Sao Jose Rio Preto, Sao Paulo, BrazilUniv Estadual Paulista, Dept Matemat Aplicada, Campus Sao Jose Rio Preto, Sao Paulo, BrazilFAPESP: 2012/21042-0CNPq: 305073/2014-1FAPESP: 2009/13832-9Taylor & Francis LtdUniversidade Federal do Rio de Janeiro (UFRJ)Universidade Estadual Paulista (Unesp)Borrego-Morell, J.Ranga, A. Sri [UNESP]2018-11-26T17:12:11Z2018-11-26T17:12:11Z2016-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article39-55application/pdfhttp://dx.doi.org/10.1080/10652469.2016.1249866Integral Transforms And Special Functions. Abingdon: Taylor & Francis Ltd, v. 28, n. 1, p. 39-55, 2016.1065-2469http://hdl.handle.net/11449/16219010.1080/10652469.2016.1249866WOS:000388742900004WOS000388742900004.pdfWeb of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengIntegral Transforms And Special Functions0,819info:eu-repo/semantics/openAccess2024-01-22T06:22:57Zoai:repositorio.unesp.br:11449/162190Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:40:11.163106Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients |
title |
Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients |
spellingShingle |
Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients Borrego-Morell, J. Orthogonal polynomials on the unit circle differential equations special functions complex analysis |
title_short |
Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients |
title_full |
Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients |
title_fullStr |
Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients |
title_full_unstemmed |
Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients |
title_sort |
Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients |
author |
Borrego-Morell, J. |
author_facet |
Borrego-Morell, J. Ranga, A. Sri [UNESP] |
author_role |
author |
author2 |
Ranga, A. Sri [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Federal do Rio de Janeiro (UFRJ) Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Borrego-Morell, J. Ranga, A. Sri [UNESP] |
dc.subject.por.fl_str_mv |
Orthogonal polynomials on the unit circle differential equations special functions complex analysis |
topic |
Orthogonal polynomials on the unit circle differential equations special functions complex analysis |
description |
Consider the linear second-order differential equation An(z) y+ B-n(z) y' + C(n)y = 0, where A(n)(z) = a(2), nz(2) + a(1,n)z + a(0), n with a(2), n = 0, a2 1, n - 4a2, na0, n = 0,. n. N or a2, n = 0, a1, n = 0,. n. N, Bn(z) = b1, n + b0, nz are polynomials with complex coefficients and Cn. C. Under some assumptions over a certain class of lowering and raising operators, we show that for a sequence of polynomials (fn)8 n = 0 orthogonal on the unit circle to satisfy the differential equation (1.1), the polynomial fn must be of a specific form involving and extension of the Gauss and confluent hypergeometric series. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-01-01 2018-11-26T17:12:11Z 2018-11-26T17:12:11Z |
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/10.1080/10652469.2016.1249866 Integral Transforms And Special Functions. Abingdon: Taylor & Francis Ltd, v. 28, n. 1, p. 39-55, 2016. 1065-2469 http://hdl.handle.net/11449/162190 10.1080/10652469.2016.1249866 WOS:000388742900004 WOS000388742900004.pdf |
url |
http://dx.doi.org/10.1080/10652469.2016.1249866 http://hdl.handle.net/11449/162190 |
identifier_str_mv |
Integral Transforms And Special Functions. Abingdon: Taylor & Francis Ltd, v. 28, n. 1, p. 39-55, 2016. 1065-2469 10.1080/10652469.2016.1249866 WOS:000388742900004 WOS000388742900004.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Integral Transforms And Special Functions 0,819 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
39-55 application/pdf |
dc.publisher.none.fl_str_mv |
Taylor & Francis Ltd |
publisher.none.fl_str_mv |
Taylor & Francis Ltd |
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 |
|
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1808129541125701632 |