A generalization of André-Jeannin’s symmetric identity

In 1997, Richard André-Jeannin obtained a symmetric identity involving the reciprocal of the Horadam numbers , defined by a three-term recurrence = with constant coefficients. In this paper, we extend this identity to sequences satisfying a three-term recurrence = + with arbitrary coefficients. Then...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Pure mathematics and applications Jg. 27; H. 1; S. 98 - 118
1. Verfasser: Munarini, Emanuele
Format: Journal Article
Sprache:Englisch
Ungarisch
Veröffentlicht: Firenze Sciendo 01.07.2018
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Schlagworte:
Chebyshev polynomials
combinatorial sums
Fibonacci numbers
Fibonacci polynomials
Jacobsthal numbers
Jacobsthal polynomials
Lucas numbers
Lucas polynomials
Morgan-Voyce polynomials
Pell numbers
Pell polynomials
Primary 05A19
Secondary 05A30, 11B65
sums of reciprocals
three-term recurrences
ISSN:1788-800X, 1788-800X
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract In 1997, Richard André-Jeannin obtained a symmetric identity involving the reciprocal of the Horadam numbers , defined by a three-term recurrence = with constant coefficients. In this paper, we extend this identity to sequences satisfying a three-term recurrence = + with arbitrary coefficients. Then, we specialize such an identity to several -polynomials of combinatorial interest, such as the -Fibonacci, -Lucas, -Pell, -Jacobsthal, -Chebyshev and -Morgan-Voyce polynomials.
AbstractList In 1997, Richard André-Jeannin obtained a symmetric identity involving the reciprocal of the Horadam numbers W n , defined by a three-term recurrence W n +2 = P W n +1 − QW n with constant coefficients. In this paper, we extend this identity to sequences {a n } n ∈ℕ satisfying a three-term recurrence a n +2 = p n +1 a n +1 + q n +1 a n with arbitrary coefficients. Then, we specialize such an identity to several q -polynomials of combinatorial interest, such as the q -Fibonacci, q -Lucas, q -Pell, q -Jacobsthal, q -Chebyshev and q -Morgan-Voyce polynomials.
In 1997, Richard André-Jeannin obtained a symmetric identity involving the reciprocal of the Horadam numbers Wn, defined by a three-term recurrence Wn+2 = P Wn+1− QWn with constant coefficients. In this paper, we extend this identity to sequences {an}n∈ℕ satisfying a three-term recurrence an+2 = pn+1an+1 + qn+1an with arbitrary coefficients. Then, we specialize such an identity to several q-polynomials of combinatorial interest, such as the q-Fibonacci, q-Lucas, q-Pell, q-Jacobsthal, q-Chebyshev and q-Morgan-Voyce polynomials.
In 1997, Richard André-Jeannin obtained a symmetric identity involving the reciprocal of the Horadam numbers , defined by a three-term recurrence = with constant coefficients. In this paper, we extend this identity to sequences satisfying a three-term recurrence = + with arbitrary coefficients. Then, we specialize such an identity to several -polynomials of combinatorial interest, such as the -Fibonacci, -Lucas, -Pell, -Jacobsthal, -Chebyshev and -Morgan-Voyce polynomials.
Author Munarini, Emanuele
Author_xml – sequence: 1
  givenname: Emanuele
  surname: Munarini
  fullname: Munarini, Emanuele
  email: emanuele.munarini@polimi.it
  organization: Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
BookMark eNp9kMFKw0AQhhepYK29eg54Tp3d7Wa3eCpFq1LwouBt2SSzJaXZ1N0EiSdfw0fwOXwTn8SECnoQ5zJz-L9_4DsmA1c5JOSUwoQKKs53TWliBlTEAEwdkCGVSsUK4HHw6z4i4xA20I2Qs4SrIZnNozU69GZbvJi6qFxU2Wjucv_xHt-ica5wn69vIQptWWLtiywqcnR1Ubcn5NCabcDx9x6Rh6vL-8V1vLpb3izmqzijSqqY8SmnNpeYcgMUhWBSTa01qUmttZTlQhqD04RLAJ4Ym6eWIWIKDEFmLOEjcrbv3fnqqcFQ603VeNe91JxJDh2YwL8pKiRNFJd912SfynwVgkerd74ojW81Bd171L1H3XvUvccOuNgDz2Zbo89x7Zu2O37a_waZpDPFvwDZzHxl
Cites_doi 10.1080/00150517.1966.12431395
10.1016/j.aim.2005.04.006
10.1007/s00026-011-0067-8
10.1016/S0012-365X(01)00475-7
10.1080/00150517.2005.12428364
10.1109/TCT.1959.1086564
10.1080/00150517.1968.12431247
10.2140/pjm.1983.104.269
10.1215/S0012-7094-65-03244-8
10.1080/00150517.1997.12429031
10.2478/s11533-011-0002-6
10.1080/00150517.1975.12430654
10.1080/00150517.1965.12431416
10.1016/j.disc.2006.03.067
10.1080/00150517.1974.12430696
10.1080/00150517.1994.12429229
10.1016/j.ejc.2008.01.015
ContentType Journal Article
Copyright 2018. This work is published under http://creativecommons.org/licenses/by-nc-nd/4.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
2018. This work is published under http://creativecommons.org/licenses/by-nc-nd/4.0 (the "License"). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2018. This work is published under http://creativecommons.org/licenses/by-nc-nd/4.0 (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
– notice: 2018. This work is published under http://creativecommons.org/licenses/by-nc-nd/4.0 (the "License"). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID AAYXX
CITATION
ABUWG
AFKRA
AZQEC
BENPR
CCPQU
DWQXO
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQQKQ
PQUKI
PRINS
DOI 10.1515/puma-2015-0028
DatabaseName CrossRef
ProQuest Central (Alumni)
ProQuest Central UK/Ireland
ProQuest Central Essentials
ProQuest Central
ProQuest One Community College
ProQuest Central
ProQuest Central Premium
ProQuest One Academic
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
DatabaseTitle CrossRef
Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
ProQuest One Community College
ProQuest Central China
ProQuest Central
ProQuest One Academic UKI Edition
ProQuest Central Korea
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
DatabaseTitleList CrossRef
Publicly Available Content Database
Publicly Available Content Database
Database_xml – sequence: 1
  dbid: PIMPY
  name: Publicly Available Content Database
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1788-800X
EndPage 118
ExternalDocumentID 10_1515_puma_2015_0028
10_1515_puma_2015_002827198
GroupedDBID 9WM
AATOW
ABFKT
ACGFS
ADBLJ
AFFHD
AFKRA
AHGSO
AIKXB
ALMA_UNASSIGNED_HOLDINGS
BENPR
CCPQU
EBS
EJD
KQ8
PHGZM
PHGZT
PIMPY
QD8
AAYXX
CITATION
ABUWG
AZQEC
DWQXO
PKEHL
PQEST
PQQKQ
PQUKI
PRINS
ID FETCH-LOGICAL-c1878-23431fd7eb3a01e552784ffababfff12d57aae46370036afdbf2eeeb02e07c263
IEDL.DBID BENPR
ISSN 1788-800X
IngestDate Thu Nov 20 01:19:22 EST 2025
Sun Oct 19 01:25:46 EDT 2025
Sat Nov 29 03:33:43 EST 2025
Sat Nov 29 01:30:54 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 1
Language English
Hungarian
License This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
http://creativecommons.org/licenses/by-nc-nd/4.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c1878-23431fd7eb3a01e552784ffababfff12d57aae46370036afdbf2eeeb02e07c263
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
OpenAccessLink https://www.proquest.com/docview/3273037060?pq-origsite=%requestingapplication%
PQID 3157168376
PQPubID 6771863
PageCount 21
ParticipantIDs proquest_journals_3273037060
proquest_journals_3157168376
crossref_primary_10_1515_puma_2015_0028
walterdegruyter_journals_10_1515_puma_2015_002827198
PublicationCentury 2000
PublicationDate 2018-07-01
PublicationDateYYYYMMDD 2018-07-01
PublicationDate_xml – month: 07
  year: 2018
  text: 2018-07-01
  day: 01
PublicationDecade 2010
PublicationPlace Firenze
PublicationPlace_xml – name: Firenze
PublicationTitle Pure mathematics and applications
PublicationYear 2018
Publisher Sciendo
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Publisher_xml – name: Sciendo
– name: De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
References 2025012100174595589_j_puma-2015-0028_ref_009_w2aab3b7b5b1b6b1ab1ab9Aa
2025012100174595589_j_puma-2015-0028_ref_004_w2aab3b7b5b1b6b1ab1ab4Aa
2025012100174595589_j_puma-2015-0028_ref_017_w2aab3b7b5b1b6b1ab1ac17Aa
2025012100174595589_j_puma-2015-0028_ref_015_w2aab3b7b5b1b6b1ab1ac15Aa
2025012100174595589_j_puma-2015-0028_ref_008_w2aab3b7b5b1b6b1ab1ab8Aa
2025012100174595589_j_puma-2015-0028_ref_011_w2aab3b7b5b1b6b1ab1ac11Aa
2025012100174595589_j_puma-2015-0028_ref_003_w2aab3b7b5b1b6b1ab1ab3Aa
2025012100174595589_j_puma-2015-0028_ref_010_w2aab3b7b5b1b6b1ab1ac10Aa
2025012100174595589_j_puma-2015-0028_ref_007_w2aab3b7b5b1b6b1ab1ab7Aa
2025012100174595589_j_puma-2015-0028_ref_013_w2aab3b7b5b1b6b1ab1ac13Aa
2025012100174595589_j_puma-2015-0028_ref_002_w2aab3b7b5b1b6b1ab1ab2Aa
2025012100174595589_j_puma-2015-0028_ref_016_w2aab3b7b5b1b6b1ab1ac16Aa
2025012100174595589_j_puma-2015-0028_ref_018_w2aab3b7b5b1b6b1ab1ac18Aa
2025012100174595589_j_puma-2015-0028_ref_006_w2aab3b7b5b1b6b1ab1ab6Aa
2025012100174595589_j_puma-2015-0028_ref_012_w2aab3b7b5b1b6b1ab1ac12Aa
2025012100174595589_j_puma-2015-0028_ref_001_w2aab3b7b5b1b6b1ab1ab1Aa
2025012100174595589_j_puma-2015-0028_ref_005_w2aab3b7b5b1b6b1ab1ab5Aa
2025012100174595589_j_puma-2015-0028_ref_020_w2aab3b7b5b1b6b1ab1ac20Aa
2025012100174595589_j_puma-2015-0028_ref_014_w2aab3b7b5b1b6b1ab1ac14Aa
2025012100174595589_j_puma-2015-0028_ref_019_w2aab3b7b5b1b6b1ab1ac19Aa
References_xml – ident: 2025012100174595589_j_puma-2015-0028_ref_019_w2aab3b7b5b1b6b1ab1ac19Aa
  doi: 10.1080/00150517.1966.12431395
– ident: 2025012100174595589_j_puma-2015-0028_ref_011_w2aab3b7b5b1b6b1ab1ac11Aa
  doi: 10.1016/j.aim.2005.04.006
– ident: 2025012100174595589_j_puma-2015-0028_ref_003_w2aab3b7b5b1b6b1ab1ab3Aa
  doi: 10.1007/s00026-011-0067-8
– ident: 2025012100174595589_j_puma-2015-0028_ref_016_w2aab3b7b5b1b6b1ab1ac16Aa
  doi: 10.1016/S0012-365X(01)00475-7
– ident: 2025012100174595589_j_puma-2015-0028_ref_014_w2aab3b7b5b1b6b1ab1ac14Aa
  doi: 10.1080/00150517.2005.12428364
– ident: 2025012100174595589_j_puma-2015-0028_ref_013_w2aab3b7b5b1b6b1ab1ac13Aa
  doi: 10.1109/TCT.1959.1086564
– ident: 2025012100174595589_j_puma-2015-0028_ref_020_w2aab3b7b5b1b6b1ab1ac20Aa
  doi: 10.1080/00150517.1968.12431247
– ident: 2025012100174595589_j_puma-2015-0028_ref_001_w2aab3b7b5b1b6b1ab1ab1Aa
  doi: 10.2140/pjm.1983.104.269
– ident: 2025012100174595589_j_puma-2015-0028_ref_017_w2aab3b7b5b1b6b1ab1ac17Aa
– ident: 2025012100174595589_j_puma-2015-0028_ref_009_w2aab3b7b5b1b6b1ab1ab9Aa
  doi: 10.1215/S0012-7094-65-03244-8
– ident: 2025012100174595589_j_puma-2015-0028_ref_002_w2aab3b7b5b1b6b1ab1ab2Aa
  doi: 10.1080/00150517.1997.12429031
– ident: 2025012100174595589_j_puma-2015-0028_ref_012_w2aab3b7b5b1b6b1ab1ac12Aa
  doi: 10.2478/s11533-011-0002-6
– ident: 2025012100174595589_j_puma-2015-0028_ref_005_w2aab3b7b5b1b6b1ab1ab5Aa
  doi: 10.1080/00150517.1975.12430654
– ident: 2025012100174595589_j_puma-2015-0028_ref_008_w2aab3b7b5b1b6b1ab1ab8Aa
  doi: 10.1080/00150517.1965.12431416
– ident: 2025012100174595589_j_puma-2015-0028_ref_010_w2aab3b7b5b1b6b1ab1ac10Aa
– ident: 2025012100174595589_j_puma-2015-0028_ref_018_w2aab3b7b5b1b6b1ab1ac18Aa
– ident: 2025012100174595589_j_puma-2015-0028_ref_015_w2aab3b7b5b1b6b1ab1ac15Aa
  doi: 10.1016/j.disc.2006.03.067
– ident: 2025012100174595589_j_puma-2015-0028_ref_004_w2aab3b7b5b1b6b1ab1ab4Aa
  doi: 10.1080/00150517.1974.12430696
– ident: 2025012100174595589_j_puma-2015-0028_ref_006_w2aab3b7b5b1b6b1ab1ab6Aa
  doi: 10.1080/00150517.1994.12429229
– ident: 2025012100174595589_j_puma-2015-0028_ref_007_w2aab3b7b5b1b6b1ab1ab7Aa
  doi: 10.1016/j.ejc.2008.01.015
SSID ssj0000579638
Score 2.031503
Snippet In 1997, Richard André-Jeannin obtained a symmetric identity involving the reciprocal of the Horadam numbers , defined by a three-term recurrence = with...
In 1997, Richard André-Jeannin obtained a symmetric identity involving the reciprocal of the Horadam numbers W n , defined by a three-term recurrence W n +2 =...
In 1997, Richard André-Jeannin obtained a symmetric identity involving the reciprocal of the Horadam numbers Wn, defined by a three-term recurrence Wn+2 = P...
SourceID proquest
crossref
walterdegruyter
SourceType Aggregation Database
Index Database
Publisher
StartPage 98
SubjectTerms Chebyshev polynomials
combinatorial sums
Fibonacci numbers
Fibonacci polynomials
Jacobsthal numbers
Jacobsthal polynomials
Lucas numbers
Lucas polynomials
Morgan-Voyce polynomials
Pell numbers
Pell polynomials
Primary 05A19
Secondary 05A30, 11B65
sums of reciprocals
three-term recurrences
Title A generalization of André-Jeannin’s symmetric identity
URI https://reference-global.com/article/10.1515/puma-2015-0028
https://www.proquest.com/docview/3157168376
https://www.proquest.com/docview/3273037060
Volume 27
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVPQU
  databaseName: ProQuest Central
  customDbUrl:
  eissn: 1788-800X
  dateEnd: 20201231
  omitProxy: false
  ssIdentifier: ssj0000579638
  issn: 1788-800X
  databaseCode: BENPR
  dateStart: 20170101
  isFulltext: true
  titleUrlDefault: https://www.proquest.com/central
  providerName: ProQuest
– providerCode: PRVPQU
  databaseName: Publicly Available Content Database
  customDbUrl:
  eissn: 1788-800X
  dateEnd: 20201231
  omitProxy: false
  ssIdentifier: ssj0000579638
  issn: 1788-800X
  databaseCode: PIMPY
  dateStart: 20170101
  isFulltext: true
  titleUrlDefault: http://search.proquest.com/publiccontent
  providerName: ProQuest
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV27TsMwFLWgZYChvEWhoAxITBZNnMTJhApqBYhWFQJUpsjxo3Tog6YFdeM3-AS-gz_hS7hO3FagioUpQ-zEuvfa92H7HISOOaW-R-0Qh1z42BXCwwG3OY49B9pTrkhK9_ZwQxuNoNUKm6bglphjldM1MV2oRZ_rGvkpAT9bJhrr5WzwjDVrlN5dNRQayyivkcrAzvPn1UbzdlZlSa9aksCgNYLvPh2MuwxMw_awTjd-eqN5iFl4TTerhWwPx5PRdHM09Tm19f-OdgMVTLRpVTLz2ERLT-MttFafQbUm2yisWO0MetrcyLT6ytLHHD8_8LVMGY2-3t4TK5l0u5p9i1ud7G7vZAfd16p3F5fY8ClgbgeQLDoEogUlKOTPrGxLjb0WuEqxmMVKKdsRHmVMuj6MG_waUyJWjpQyLjuyTLnjk12U6_V7cg9ZAvIuG_pIEghXUBITh0lfCeikiGBeEZ1M5RoNMtiMSKcboIFIayDSGoi0BoqoNJVgZKZPEhEb7MeH3Nlf_Hom3SJyf2lq3mrx_xwwzGD_768eoFVoH2SncksoNxqO5SFa4S-jTjI8MjYGz-ZVvfn4DTsb4QQ
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3NbhMxEB61KVLh0EIpIlDKHkA9Wd21d9fOAaEKqJrmRzkEVE6L1z-hhzQhm1Dlxmv0EXrpS_RNeBLG-5OIKuLWA-f1n_b7POPxeGYA3ijO44gHDdJQOiah1hERKlAkjSi258qyvNzblzbvdsXZWaO3BjdVLIx7VlnJxFxQ65Fyd-SHDPWsz1yul_fjH8RVjXLe1aqERkGLlplfosmWvWt-RHzfUnr8qf_hhJRVBYgKBJpMlKHOtJqjFSn9wLgMZCK0VqYytdYGVEdcShPGOBdKd2l1aqkxJvWp8bmiMcNx12EjRLL7NdjoNTu9r4tbnTy0k4kyOySeFQ7Hs6FEKgYRcebN39pveaTdusyd49oMJrP5tHLG5jruePt_-zuPYas8TXtHBf2fwNr32Q486ixS0WZPoXHkDYrU2mXEqTeynnvGeXtNTk1esen3r6vMy-bDoasuprzzInZ5vguf72Xtz6B2Mbowz8HTaFcG2McwoUPNWcqoNLHV2MkyLaM6HFQ4JuMiLUjizClEPHGIJw7xxCFeh70KsaQUD1nCAtwfsUDhvvrzAs06hHeYsWy1ej6KG0-8-Peor2HzpN9pJ-1mt_USHmJfUbxA3oPadDIzr-CB-jk9zyb7Jb89-HbfpPkD158-ig
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+generalization+of+Andr%C3%A9-Jeannin%E2%80%99s+symmetric+identity&rft.jtitle=Pure+mathematics+and+applications&rft.au=Munarini%2C+Emanuele&rft.date=2018-07-01&rft.pub=Sciendo&rft.eissn=1788-800X&rft.volume=27&rft.issue=1&rft.spage=98&rft.epage=118&rft_id=info:doi/10.1515%2Fpuma-2015-0028&rft.externalDBID=n%2Fa&rft.externalDocID=10_1515_puma_2015_002827198
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1788-800X&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1788-800X&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1788-800X&client=summon