Publicação
On the Leonardo quaternions sequence
| datacite.subject.fos | Ciências Naturais::Matemáticas | |
| dc.contributor.author | Beites, Patrícia Damas | |
| dc.contributor.author | Catarino, Paula Maria Machado Cruz | |
| dc.date.accessioned | 2026-01-20T10:56:20Z | |
| dc.date.available | 2026-01-20T10:56:20Z | |
| dc.date.issued | 2024-08-27 | |
| dc.description.abstract | In the present work, a new sequence of quaternions related to the Leonardo numbers – named the Leonardo quaternions sequence – is defined and studied. Binet’s formula and certain sum and binomial-sum identities, some of which derived from the mentioned formula, are established. Tagiuri-Vajda’s identity and, as consequences, Catalan’s identity, d’Ocagne’s identity and Cassini’s identity are presented. Furthermore, applying Catalan’s identity, and the connection between composition algebras and vector cross product algebras, Gelin-Cesàro’s identity is also stated and proved. Finally, the generating function, the exponential generating function and the Poisson generating function are deduced. In addition to the results on Leonardo quaternions, known results on Leonardo numbers and on Fibonacci quaternions are extended. | eng |
| dc.description.sponsorship | UIDB/00212/2020, MTM2017-83506-C2-2-P, UIDB/00013/2020, UIDP/00013/2020, UID/CED/00194/2020 | |
| dc.identifier.citation | Beites, P., & Catarino, P. M. M. C. (2024). On the Leonardo quaternions sequence. Hacettepe Journal of Mathematics and Statistics, 53(4), 1001-1023. https://doi.org/10.15672/hujms.1197693 | |
| dc.identifier.doi | 10.15672/hujms.1197693 | |
| dc.identifier.eissn | 2651-477X | |
| dc.identifier.issn | 2651-477X | |
| dc.identifier.uri | http://hdl.handle.net/10400.6/19693 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.relation | Center of Mathematics and Applications of University of Beira Interior | |
| dc.relation | Research Centre Didactics and Technology in the Education of Trainers | |
| dc.relation.hasversion | https://dergipark.org.tr/en/pub/hujms/article/1197693 | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Leonardo numbers | |
| dc.subject | Leonardo quaternions | |
| dc.subject | Binet’s formula | |
| dc.subject | Generating function | |
| dc.title | On the Leonardo quaternions sequence | por |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardTitle | Center of Mathematics and Applications of University of Beira Interior | |
| oaire.awardTitle | Research Centre Didactics and Technology in the Education of Trainers | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00212%2F2020/PT | |
| oaire.awardURI | http://hdl.handle.net/10400.6/19673 | |
| oaire.citation.endPage | 1023 | |
| oaire.citation.issue | 4 | |
| oaire.citation.startPage | 1001 | |
| oaire.citation.title | Hacettepe Journal of Mathematics and Statistics | |
| oaire.citation.volume | 53 | |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| oaire.fundingStream | Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento Programático | |
| oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |
| person.familyName | Beites | |
| person.familyName | Catarino | |
| person.givenName | Patrícia Damas | |
| person.givenName | Paula Maria Machado Cruz | |
| person.identifier | urn:authenticus_id:https://www.authenticus.pt/en/UserGroups/myData/589 | |
| person.identifier.ciencia-id | 591A-8D9A-73CE | |
| person.identifier.ciencia-id | 291D-DC3F-A2CD | |
| person.identifier.gsid | https://scholar.google.com/citations?user=SFM-4ywAAAAJ | |
| person.identifier.orcid | 0000-0003-0266-7055 | |
| person.identifier.orcid | 0000-0001-6917-5093 | |
| person.identifier.rid | K-5772-2017 | |
| person.identifier.rid | H-3190-2014 | |
| person.identifier.scopus-author-id | 37041170800 | |
| person.identifier.scopus-author-id | 55899791800 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
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