Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/45794 |
Resumo: | This paper aims to give new insights into homogeneous hypercomplex Appell polynomials through the study of some interesting arithmetical properties of their coefficients. Here Appell polynomials are introduced as constituting a hypercomplex generalized geometric series whose fundamental role sometimes seems to have been neglected. Surprisingly, in the simplest non-commutative case their rational coefficient sequence reduces to a coefficient sequence S used in a celebrated theorem on positive trigonometric sums by Vietoris (Sitzungsber Österr Akad Wiss 167:125–135, 1958). For S a generating function is obtained which allows to derive an interesting relation to a result deduced by Askey and Steinig (Trans AMS 187(1):295–307, 1974) about some trigonometric series. The further study of S is concerned with a sequence of integers leading to its irreducible representation and its relation to central binomial coefficients. |
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Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequenceVietoris’ number sequenceMonogenic Appell polynomialsGenerating functionsCiências Naturais::MatemáticasScience & TechnologyThis paper aims to give new insights into homogeneous hypercomplex Appell polynomials through the study of some interesting arithmetical properties of their coefficients. Here Appell polynomials are introduced as constituting a hypercomplex generalized geometric series whose fundamental role sometimes seems to have been neglected. Surprisingly, in the simplest non-commutative case their rational coefficient sequence reduces to a coefficient sequence S used in a celebrated theorem on positive trigonometric sums by Vietoris (Sitzungsber Österr Akad Wiss 167:125–135, 1958). For S a generating function is obtained which allows to derive an interesting relation to a result deduced by Askey and Steinig (Trans AMS 187(1):295–307, 1974) about some trigonometric series. The further study of S is concerned with a sequence of integers leading to its irreducible representation and its relation to central binomial coefficients.The work of the first and third authors was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e Tecnologia”), within project PEstOE/MAT/UI4106/2013. The work of the second author was supported by Portuguese funds through the CMAT - Centre of Mathematics and FCT within the Project UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersionSpringer VerlagUniversidade do MinhoCação, IsabelFalcão, M. I.Malonek, Helmuth20172017-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/45794eng1661-82541661-826210.1007/s11785-017-0649-5http://dx.doi.org/10.1007/s11785-017-0649-5info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:03:13Zoai:repositorium.sdum.uminho.pt:1822/45794Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T18:53:18.806577Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence |
title |
Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence |
spellingShingle |
Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence Cação, Isabel Vietoris’ number sequence Monogenic Appell polynomials Generating functions Ciências Naturais::Matemáticas Science & Technology |
title_short |
Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence |
title_full |
Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence |
title_fullStr |
Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence |
title_full_unstemmed |
Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence |
title_sort |
Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence |
author |
Cação, Isabel |
author_facet |
Cação, Isabel Falcão, M. I. Malonek, Helmuth |
author_role |
author |
author2 |
Falcão, M. I. Malonek, Helmuth |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Cação, Isabel Falcão, M. I. Malonek, Helmuth |
dc.subject.por.fl_str_mv |
Vietoris’ number sequence Monogenic Appell polynomials Generating functions Ciências Naturais::Matemáticas Science & Technology |
topic |
Vietoris’ number sequence Monogenic Appell polynomials Generating functions Ciências Naturais::Matemáticas Science & Technology |
description |
This paper aims to give new insights into homogeneous hypercomplex Appell polynomials through the study of some interesting arithmetical properties of their coefficients. Here Appell polynomials are introduced as constituting a hypercomplex generalized geometric series whose fundamental role sometimes seems to have been neglected. Surprisingly, in the simplest non-commutative case their rational coefficient sequence reduces to a coefficient sequence S used in a celebrated theorem on positive trigonometric sums by Vietoris (Sitzungsber Österr Akad Wiss 167:125–135, 1958). For S a generating function is obtained which allows to derive an interesting relation to a result deduced by Askey and Steinig (Trans AMS 187(1):295–307, 1974) about some trigonometric series. The further study of S is concerned with a sequence of integers leading to its irreducible representation and its relation to central binomial coefficients. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017 2017-01-01T00:00:00Z |
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://hdl.handle.net/1822/45794 |
url |
http://hdl.handle.net/1822/45794 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1661-8254 1661-8262 10.1007/s11785-017-0649-5 http://dx.doi.org/10.1007/s11785-017-0649-5 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Springer Verlag |
publisher.none.fl_str_mv |
Springer Verlag |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799132311752540160 |