BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS
Autor(a) principal: | |
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Data de Publicação: | 2012 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
DOI: | 10.1090/S0002-9939-2011-11066-9 |
Texto Completo: | http://dx.doi.org/10.1090/S0002-9939-2011-11066-9 http://hdl.handle.net/11449/21806 |
Resumo: | A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the orthogonality properties of the sequence of polynomials {(2)Phi(1)(q(-n), q(b+1); q(-c+b-n); q,q(-c+d-1)z)}(n=0)(infinity), where 0 < q < 1 and the complex parameters b, c and d are such that b not equal -1, -2, ... , c - b + 1 not equal -1, -2, ... , Re(d) > 0 and Re(c - d + 2) > 0. Explicit expressions for the recurrence coefficients, moments, orthogonality and also asymptotic properties are given. By a special choice of the parameters, results regarding a class of Szego polynomials are also derived. |
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Repositório Institucional da UNESP |
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BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALSBasic hypergeometric functionsContinued fractionsOrthogonal Laurent polynomialsSzegö polynomialsA three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the orthogonality properties of the sequence of polynomials {(2)Phi(1)(q(-n), q(b+1); q(-c+b-n); q,q(-c+d-1)z)}(n=0)(infinity), where 0 < q < 1 and the complex parameters b, c and d are such that b not equal -1, -2, ... , c - b + 1 not equal -1, -2, ... , Re(d) > 0 and Re(c - d + 2) > 0. Explicit expressions for the recurrence coefficients, moments, orthogonality and also asymptotic properties are given. By a special choice of the parameters, results regarding a class of Szego polynomials are also derived.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)European CommunityConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Estadual Paulista, UNESP, IBILCE, Dept Ciencias Comp & Estat, BR-15054000 Sao Jose do Rio Preto, SP, BrazilUniv Vigo, Dept Matemat Aplicada 2, ETSI Ind, Vigo 36310, SpainUniv Estadual Paulista, UNESP, IBILCE, Dept Ciencias Comp & Estat, BR-15054000 Sao Jose do Rio Preto, SP, BrazilAmer Mathematical SocUniversidade Estadual Paulista (Unesp)Univ VigoCosta, Marisa S. [UNESP]Godoy, EduardoLamblem, Regina L.Sri Ranga, A. [UNESP]2014-05-20T14:01:47Z2014-05-20T14:01:47Z2012-06-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article2075-2089application/pdfhttp://dx.doi.org/10.1090/S0002-9939-2011-11066-9Proceedings of The American Mathematical Society. Providence: Amer Mathematical Soc, v. 140, n. 6, p. 2075-2089, 2012.0002-9939http://hdl.handle.net/11449/2180610.1090/S0002-9939-2011-11066-9WOS:000303970700022WOS000303970700022.pdf3587123309745610Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengProceedings of the American Mathematical Society0.7071,183info:eu-repo/semantics/openAccess2023-12-24T06:16:21Zoai:repositorio.unesp.br:11449/21806Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T21:10:03.496318Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS |
title |
BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS |
spellingShingle |
BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS Costa, Marisa S. [UNESP] Basic hypergeometric functions Continued fractions Orthogonal Laurent polynomials Szegö polynomials Costa, Marisa S. [UNESP] Basic hypergeometric functions Continued fractions Orthogonal Laurent polynomials Szegö polynomials |
title_short |
BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS |
title_full |
BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS |
title_fullStr |
BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS |
title_full_unstemmed |
BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS |
title_sort |
BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS |
author |
Costa, Marisa S. [UNESP] |
author_facet |
Costa, Marisa S. [UNESP] Costa, Marisa S. [UNESP] Godoy, Eduardo Lamblem, Regina L. Sri Ranga, A. [UNESP] Godoy, Eduardo Lamblem, Regina L. Sri Ranga, A. [UNESP] |
author_role |
author |
author2 |
Godoy, Eduardo Lamblem, Regina L. Sri Ranga, A. [UNESP] |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Univ Vigo |
dc.contributor.author.fl_str_mv |
Costa, Marisa S. [UNESP] Godoy, Eduardo Lamblem, Regina L. Sri Ranga, A. [UNESP] |
dc.subject.por.fl_str_mv |
Basic hypergeometric functions Continued fractions Orthogonal Laurent polynomials Szegö polynomials |
topic |
Basic hypergeometric functions Continued fractions Orthogonal Laurent polynomials Szegö polynomials |
description |
A three-complex-parameter class of orthogonal Laurent polynomials on the unit circle associated with basic hypergeometric or q-hypergeometric functions is considered. To be precise, we consider the orthogonality properties of the sequence of polynomials {(2)Phi(1)(q(-n), q(b+1); q(-c+b-n); q,q(-c+d-1)z)}(n=0)(infinity), where 0 < q < 1 and the complex parameters b, c and d are such that b not equal -1, -2, ... , c - b + 1 not equal -1, -2, ... , Re(d) > 0 and Re(c - d + 2) > 0. Explicit expressions for the recurrence coefficients, moments, orthogonality and also asymptotic properties are given. By a special choice of the parameters, results regarding a class of Szego polynomials are also derived. |
publishDate |
2012 |
dc.date.none.fl_str_mv |
2012-06-01 2014-05-20T14:01:47Z 2014-05-20T14:01:47Z |
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/10.1090/S0002-9939-2011-11066-9 Proceedings of The American Mathematical Society. Providence: Amer Mathematical Soc, v. 140, n. 6, p. 2075-2089, 2012. 0002-9939 http://hdl.handle.net/11449/21806 10.1090/S0002-9939-2011-11066-9 WOS:000303970700022 WOS000303970700022.pdf 3587123309745610 |
url |
http://dx.doi.org/10.1090/S0002-9939-2011-11066-9 http://hdl.handle.net/11449/21806 |
identifier_str_mv |
Proceedings of The American Mathematical Society. Providence: Amer Mathematical Soc, v. 140, n. 6, p. 2075-2089, 2012. 0002-9939 10.1090/S0002-9939-2011-11066-9 WOS:000303970700022 WOS000303970700022.pdf 3587123309745610 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Proceedings of the American Mathematical Society 0.707 1,183 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
2075-2089 application/pdf |
dc.publisher.none.fl_str_mv |
Amer Mathematical Soc |
publisher.none.fl_str_mv |
Amer Mathematical Soc |
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_ |
1822182266937278464 |
dc.identifier.doi.none.fl_str_mv |
10.1090/S0002-9939-2011-11066-9 |