On generalized Vietoris’ number sequences
Autor(a) principal: | |
---|---|
Data de Publicação: | 2019 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/1822/62821 |
Resumo: | Recently, by using methods of hypercomplex function theory, the authors have shown that a certain sequence S of rational numbers (Vietoris’ sequence) combines seemingly disperse subjects in real, complex and hypercomplex analysis. This sequence appeared for the first time in a theorem by Vietoris (1958) with important applications in harmonic analysis (Askey/Steinig, 1974) and in the theory of stable holomorphic functions (Ruscheweyh/Salinas, 2004). A non-standard application of Clifford algebra tools for defining Clifford-holomorphic sequences of Appell polynomials was the hypercomplex context in which a one-parametric generalization S(n),n≥1, of S (corresponding to n=2) surprisingly showed up. Without relying on hypercomplex methods this paper demonstrates how purely real methods also lead to S(n). For arbitrary n≥1 the generating function is determined and for n=2 a particular case of a recurrence relation similar to that known for Catalan numbers is proved. |
id |
RCAP_f79d262f96280fb1af54f585d0a5a6d7 |
---|---|
oai_identifier_str |
oai:repositorium.sdum.uminho.pt:1822/62821 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
On generalized Vietoris’ number sequencesGenerating functionHypercomplex Appell polynomialsRecurrence relationVietoris’ number sequenceCiências Naturais::MatemáticasScience & TechnologyRecently, by using methods of hypercomplex function theory, the authors have shown that a certain sequence S of rational numbers (Vietoris’ sequence) combines seemingly disperse subjects in real, complex and hypercomplex analysis. This sequence appeared for the first time in a theorem by Vietoris (1958) with important applications in harmonic analysis (Askey/Steinig, 1974) and in the theory of stable holomorphic functions (Ruscheweyh/Salinas, 2004). A non-standard application of Clifford algebra tools for defining Clifford-holomorphic sequences of Appell polynomials was the hypercomplex context in which a one-parametric generalization S(n),n≥1, of S (corresponding to n=2) surprisingly showed up. Without relying on hypercomplex methods this paper demonstrates how purely real methods also lead to S(n). For arbitrary n≥1 the generating function is determined and for n=2 a particular case of a recurrence relation similar to that known for Catalan numbers is proved.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 PEst-OE/MAT/UI4106/2013. The work of the second author was supported by Portuguese funds through the CMAT - Centre of Mathematics and FCTwithin the Project UID/MAT/00013/2013Elsevier B.V.Universidade do MinhoCação, IsabelFalcão, M. I.Malonek, Helmuth R.2019-09-302019-09-30T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/62821eng0166-218X10.1016/j.dam.2018.10.017https://doi.org/10.1016/j.dam.2018.10.017info: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:RCAAP2024-11-16T01:25:31Zoai:repositorium.sdum.uminho.pt:1822/62821Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-11-16T01:25:31Repositório 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 |
On generalized Vietoris’ number sequences |
title |
On generalized Vietoris’ number sequences |
spellingShingle |
On generalized Vietoris’ number sequences Cação, Isabel Generating function Hypercomplex Appell polynomials Recurrence relation Vietoris’ number sequence Ciências Naturais::Matemáticas Science & Technology |
title_short |
On generalized Vietoris’ number sequences |
title_full |
On generalized Vietoris’ number sequences |
title_fullStr |
On generalized Vietoris’ number sequences |
title_full_unstemmed |
On generalized Vietoris’ number sequences |
title_sort |
On generalized Vietoris’ number sequences |
author |
Cação, Isabel |
author_facet |
Cação, Isabel Falcão, M. I. Malonek, Helmuth R. |
author_role |
author |
author2 |
Falcão, M. I. Malonek, Helmuth R. |
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 R. |
dc.subject.por.fl_str_mv |
Generating function Hypercomplex Appell polynomials Recurrence relation Vietoris’ number sequence Ciências Naturais::Matemáticas Science & Technology |
topic |
Generating function Hypercomplex Appell polynomials Recurrence relation Vietoris’ number sequence Ciências Naturais::Matemáticas Science & Technology |
description |
Recently, by using methods of hypercomplex function theory, the authors have shown that a certain sequence S of rational numbers (Vietoris’ sequence) combines seemingly disperse subjects in real, complex and hypercomplex analysis. This sequence appeared for the first time in a theorem by Vietoris (1958) with important applications in harmonic analysis (Askey/Steinig, 1974) and in the theory of stable holomorphic functions (Ruscheweyh/Salinas, 2004). A non-standard application of Clifford algebra tools for defining Clifford-holomorphic sequences of Appell polynomials was the hypercomplex context in which a one-parametric generalization S(n),n≥1, of S (corresponding to n=2) surprisingly showed up. Without relying on hypercomplex methods this paper demonstrates how purely real methods also lead to S(n). For arbitrary n≥1 the generating function is determined and for n=2 a particular case of a recurrence relation similar to that known for Catalan numbers is proved. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-09-30 2019-09-30T00:00:00Z |
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 |
https://hdl.handle.net/1822/62821 |
url |
https://hdl.handle.net/1822/62821 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0166-218X 10.1016/j.dam.2018.10.017 https://doi.org/10.1016/j.dam.2018.10.017 |
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 |
Elsevier B.V. |
publisher.none.fl_str_mv |
Elsevier B.V. |
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 |
repository.mail.fl_str_mv |
mluisa.alvim@gmail.com |
_version_ |
1817544446001020928 |