Asymptotics for generating functions of the Fuss-Catalan numbers

Detalhes bibliográficos
Autor(a) principal: Azevedo, Assis
Data de Publicação: 2023
Outros Autores: Azevedo, Davide Manuel Santos
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: https://hdl.handle.net/1822/89116
Resumo: We consider a certain class of polynomials with coefficients in Z_M, all of which admit a unique zero. We prove that the zero of each of those can be given by a (multiple) sum involving the coefficients and a vectorial generalization of the Fuss-Catalan numbers. We also consider the sequence of the partial sums of the generating function of the d -Fuss- Catalan numbers. Using the holonomy of this sequence, we study its asymptotic behaviour. The main difference from the known case d = 2 is, in that one, we have a “closed” expression for the generating function.
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spelling Asymptotics for generating functions of the Fuss-Catalan numbersuss-Catalan numbersasymptotic behaviorholonomic sequencepolynomial congruencevectorial Catalan numbersCiências Naturais::MatemáticasWe consider a certain class of polynomials with coefficients in Z_M, all of which admit a unique zero. We prove that the zero of each of those can be given by a (multiple) sum involving the coefficients and a vectorial generalization of the Fuss-Catalan numbers. We also consider the sequence of the partial sums of the generating function of the d -Fuss- Catalan numbers. Using the holonomy of this sequence, we study its asymptotic behaviour. The main difference from the known case d = 2 is, in that one, we have a “closed” expression for the generating function.The research of the authors were partially financed by Portuguese Funds through Fundação para a Ciência e a Tecnologia within the Projects UIDB/00013/2020 and UIDP/00013/2020.Element D.o.o.Universidade do MinhoAzevedo, AssisAzevedo, Davide Manuel Santos2023-112023-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/89116engAzevedo, A., & Azevedo, D. (2023). Asymptotics for generating functions of the Fuss-Catalan numbers. Mathematical Inequalities & Applications. Element d.o.o. http://doi.org/10.7153/mia-2023-26-511331-43431848-996610.7153/mia-2023-26-51https://files.ele-math.com/articles/mia-26-51.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:RCAAP2024-03-02T01:19:36Zoai:repositorium.sdum.uminho.pt:1822/89116Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:11:46.045290Repositório 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 Asymptotics for generating functions of the Fuss-Catalan numbers
title Asymptotics for generating functions of the Fuss-Catalan numbers
spellingShingle Asymptotics for generating functions of the Fuss-Catalan numbers
Azevedo, Assis
uss-Catalan numbers
asymptotic behavior
holonomic sequence
polynomial congruence
vectorial Catalan numbers
Ciências Naturais::Matemáticas
title_short Asymptotics for generating functions of the Fuss-Catalan numbers
title_full Asymptotics for generating functions of the Fuss-Catalan numbers
title_fullStr Asymptotics for generating functions of the Fuss-Catalan numbers
title_full_unstemmed Asymptotics for generating functions of the Fuss-Catalan numbers
title_sort Asymptotics for generating functions of the Fuss-Catalan numbers
author Azevedo, Assis
author_facet Azevedo, Assis
Azevedo, Davide Manuel Santos
author_role author
author2 Azevedo, Davide Manuel Santos
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Azevedo, Assis
Azevedo, Davide Manuel Santos
dc.subject.por.fl_str_mv uss-Catalan numbers
asymptotic behavior
holonomic sequence
polynomial congruence
vectorial Catalan numbers
Ciências Naturais::Matemáticas
topic uss-Catalan numbers
asymptotic behavior
holonomic sequence
polynomial congruence
vectorial Catalan numbers
Ciências Naturais::Matemáticas
description We consider a certain class of polynomials with coefficients in Z_M, all of which admit a unique zero. We prove that the zero of each of those can be given by a (multiple) sum involving the coefficients and a vectorial generalization of the Fuss-Catalan numbers. We also consider the sequence of the partial sums of the generating function of the d -Fuss- Catalan numbers. Using the holonomy of this sequence, we study its asymptotic behaviour. The main difference from the known case d = 2 is, in that one, we have a “closed” expression for the generating function.
publishDate 2023
dc.date.none.fl_str_mv 2023-11
2023-11-01T00:00:00Z
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/1822/89116
url https://hdl.handle.net/1822/89116
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Azevedo, A., & Azevedo, D. (2023). Asymptotics for generating functions of the Fuss-Catalan numbers. Mathematical Inequalities & Applications. Element d.o.o. http://doi.org/10.7153/mia-2023-26-51
1331-4343
1848-9966
10.7153/mia-2023-26-51
https://files.ele-math.com/articles/mia-26-51.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 Element D.o.o.
publisher.none.fl_str_mv Element D.o.o.
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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