BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS

Detalhes bibliográficos
Autor(a) principal: Costa, Marisa S. [UNESP]
Data de Publicação: 2012
Outros Autores: Godoy, Eduardo, Lamblem, Regina L., Sri Ranga, A. [UNESP]
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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spelling 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
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dc.identifier.doi.none.fl_str_mv 10.1090/S0002-9939-2011-11066-9