The generating function of the generalized Fibonacci sequence

Detalhes bibliográficos
Autor(a) principal: Gonçalves, Armando
Data de Publicação: 2015
Outros Autores: Jesus, M. N. de
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.19/3397
Resumo: Using tools of the theory of orthogonal polynomials we obtain the generating function of the generalized Fibonacci sequence established by Petronilho for a sequence of real or complex numbers {Qn} defined by Q0 = 0, Q1 = 1, Qm = ajQm−1 + bjQm−2, m ≡ j (mod k), where k ≥ 3 is a fixed integer, and a0, a1, . . . , ak−1, b0, b1, . . . , bk−1 are 2k given real or complex numbers, with bj #0 for 0 ≤ j ≤ k−1. For this sequence some convergence proprieties are obtained.
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spelling The generating function of the generalized Fibonacci sequenceOrthogonal polynomialsGenerating functionGeneralized Fibonacci sequenceUsing tools of the theory of orthogonal polynomials we obtain the generating function of the generalized Fibonacci sequence established by Petronilho for a sequence of real or complex numbers {Qn} defined by Q0 = 0, Q1 = 1, Qm = ajQm−1 + bjQm−2, m ≡ j (mod k), where k ≥ 3 is a fixed integer, and a0, a1, . . . , ak−1, b0, b1, . . . , bk−1 are 2k given real or complex numbers, with bj #0 for 0 ≤ j ≤ k−1. For this sequence some convergence proprieties are obtained.Integers 15Repositório Científico do Instituto Politécnico de ViseuGonçalves, ArmandoJesus, M. N. de2016-11-09T09:42:54Z2015-05-292015-05-29T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.19/3397engmetadata only accessinfo: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:RCAAP2023-01-16T15:26:46Zoai:repositorio.ipv.pt:10400.19/3397Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T16:42:27.908745Repositório 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 The generating function of the generalized Fibonacci sequence
title The generating function of the generalized Fibonacci sequence
spellingShingle The generating function of the generalized Fibonacci sequence
Gonçalves, Armando
Orthogonal polynomials
Generating function
Generalized Fibonacci sequence
title_short The generating function of the generalized Fibonacci sequence
title_full The generating function of the generalized Fibonacci sequence
title_fullStr The generating function of the generalized Fibonacci sequence
title_full_unstemmed The generating function of the generalized Fibonacci sequence
title_sort The generating function of the generalized Fibonacci sequence
author Gonçalves, Armando
author_facet Gonçalves, Armando
Jesus, M. N. de
author_role author
author2 Jesus, M. N. de
author2_role author
dc.contributor.none.fl_str_mv Repositório Científico do Instituto Politécnico de Viseu
dc.contributor.author.fl_str_mv Gonçalves, Armando
Jesus, M. N. de
dc.subject.por.fl_str_mv Orthogonal polynomials
Generating function
Generalized Fibonacci sequence
topic Orthogonal polynomials
Generating function
Generalized Fibonacci sequence
description Using tools of the theory of orthogonal polynomials we obtain the generating function of the generalized Fibonacci sequence established by Petronilho for a sequence of real or complex numbers {Qn} defined by Q0 = 0, Q1 = 1, Qm = ajQm−1 + bjQm−2, m ≡ j (mod k), where k ≥ 3 is a fixed integer, and a0, a1, . . . , ak−1, b0, b1, . . . , bk−1 are 2k given real or complex numbers, with bj #0 for 0 ≤ j ≤ k−1. For this sequence some convergence proprieties are obtained.
publishDate 2015
dc.date.none.fl_str_mv 2015-05-29
2015-05-29T00:00:00Z
2016-11-09T09:42:54Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.19/3397
url http://hdl.handle.net/10400.19/3397
dc.language.iso.fl_str_mv eng
language eng
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rights_invalid_str_mv metadata only access
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Integers 15
publisher.none.fl_str_mv Integers 15
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
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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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