Intrinsic properties of a non-symmetric number triangle
Autor(a) principal: | |
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Data de Publicação: | 2023 |
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/1822/87020 |
Resumo: | Several authors are currently working on generalized Appell polynomials and their applications in the framework of hypercomplex function theory in Rn+1. A few years ago, two of the authors of this paper introduced a prototype of these generalized Appell polynomials, which heavily draws on a one-parameter family of non-symmetric number triangles T (n), n ≥ 2. In this paper, we prove several new and interesting properties of finite and infinite sums constructed from entries of T (n), similar to the ordinary Pascal triangle, which is not a part of that family. In particular, we obtain a recurrence relation for a family of finite sums, analogous to the ordinary Fibonacci sequence, and derive its corresponding generating function. |
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Intrinsic properties of a non-symmetric number triangleFibonacci sequenceHypercomplex function theoryHyperge-ometric functionRecurrence relationCiências Naturais::MatemáticasSeveral authors are currently working on generalized Appell polynomials and their applications in the framework of hypercomplex function theory in Rn+1. A few years ago, two of the authors of this paper introduced a prototype of these generalized Appell polynomials, which heavily draws on a one-parameter family of non-symmetric number triangles T (n), n ≥ 2. In this paper, we prove several new and interesting properties of finite and infinite sums constructed from entries of T (n), similar to the ordinary Pascal triangle, which is not a part of that family. In particular, we obtain a recurrence relation for a family of finite sums, analogous to the ordinary Fibonacci sequence, and derive its corresponding generating function.UA - Universidade de Aveiro(UIDB/00013/2020)This work was supported by Portuguese funds through the CMAT - Research Centre of Mathematics of University of Minho - and through the CIDMA - Center of Research and De velopment in Mathematics and Applications (University of Aveiro) and the Portuguese Foun dation for Science and Technology (“FCT - Funda¸c˜ao para a Ciˆencia e Tecnologia”), within projects UIDB/00013/2020, UIDP/00013/2020, UIDB/04106/2020 and UIDP/04106/2020.University of WaterlooUniversidade do MinhoCação, IsabelMalonek, Helmuth R.Falcão, M. I.Tomaz, Graça2023-01-012023-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/87020eng1530-7638https://cs.uwaterloo.ca/journals/JIS/VOL26/Falcao/falcao5.pdfinfo: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:RCAAP2024-05-11T05:33:19Zoai:repositorium.sdum.uminho.pt:1822/87020Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-05-11T05:33:19Repositório 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 |
Intrinsic properties of a non-symmetric number triangle |
title |
Intrinsic properties of a non-symmetric number triangle |
spellingShingle |
Intrinsic properties of a non-symmetric number triangle Cação, Isabel Fibonacci sequence Hypercomplex function theory Hyperge-ometric function Recurrence relation Ciências Naturais::Matemáticas |
title_short |
Intrinsic properties of a non-symmetric number triangle |
title_full |
Intrinsic properties of a non-symmetric number triangle |
title_fullStr |
Intrinsic properties of a non-symmetric number triangle |
title_full_unstemmed |
Intrinsic properties of a non-symmetric number triangle |
title_sort |
Intrinsic properties of a non-symmetric number triangle |
author |
Cação, Isabel |
author_facet |
Cação, Isabel Malonek, Helmuth R. Falcão, M. I. Tomaz, Graça |
author_role |
author |
author2 |
Malonek, Helmuth R. Falcão, M. I. Tomaz, Graça |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Cação, Isabel Malonek, Helmuth R. Falcão, M. I. Tomaz, Graça |
dc.subject.por.fl_str_mv |
Fibonacci sequence Hypercomplex function theory Hyperge-ometric function Recurrence relation Ciências Naturais::Matemáticas |
topic |
Fibonacci sequence Hypercomplex function theory Hyperge-ometric function Recurrence relation Ciências Naturais::Matemáticas |
description |
Several authors are currently working on generalized Appell polynomials and their applications in the framework of hypercomplex function theory in Rn+1. A few years ago, two of the authors of this paper introduced a prototype of these generalized Appell polynomials, which heavily draws on a one-parameter family of non-symmetric number triangles T (n), n ≥ 2. In this paper, we prove several new and interesting properties of finite and infinite sums constructed from entries of T (n), similar to the ordinary Pascal triangle, which is not a part of that family. In particular, we obtain a recurrence relation for a family of finite sums, analogous to the ordinary Fibonacci sequence, and derive its corresponding generating function. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-01-01 2023-01-01T00:00:00Z |
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 |
https://hdl.handle.net/1822/87020 |
url |
https://hdl.handle.net/1822/87020 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1530-7638 https://cs.uwaterloo.ca/journals/JIS/VOL26/Falcao/falcao5.pdf |
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 |
University of Waterloo |
publisher.none.fl_str_mv |
University of Waterloo |
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_ |
1817544660810203136 |