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On Quaternions with Higher Order Jacobsthal Numbers Components

ArticleAçık Erişim

Özet

In this study, we present higher order Jacobsthal numbers. Then we define higher order Jacobsthal quaternions by using higher order Jacobsthal numbers. We give the concept of the norm and conjugate for these quaternions. We express and prove some propositions related to these quaternions. Also, we find the recurrence relation, the Binet formula and the generating function for these quaternions. Finally, we calculate Cassini, Catalan, Vajda and d’Ocagne identities for higher order Jacobsthal quaternions. © 2023, Gazi Universitesi. All rights reserved.

Anahtar Kelimeler

Binet formulaExponential generating functionsHigher order Jacobsthal numbersHigher order Jacobsthal quaternionsBinet formulasHigh order jacobsthal numberHigh order jacobsthal quaternionHigh-orderHigher-orderJacobsthal numbersRecurrence relations
RDL Kalıcı Bağlantı (PID)
https://rdlopen.rawdatalibrary.net/r/ebyu/12478Resmi atıflarda kullanılan kalıcı adres
DOI
https://doi.org/10.35378/gujs.1002454Yayıncı resmi DOI adresi
Tam Kayıt
AlanDeğerDil
dc.contributor.authorOzkan, Engin
dc.contributor.authorUysal, Mine
dc.date.accessioned2026-10-18T20:27:22.642133725Z
dc.date.available2026-10-18T20:27:22.642133725Z
dc.date.issued2023
dc.description.abstractIn this study, we present higher order Jacobsthal numbers. Then we define higher order Jacobsthal quaternions by using higher order Jacobsthal numbers. We give the concept of the norm and conjugate for these quaternions. We express and prove some propositions related to these quaternions. Also, we find the recurrence relation, the Binet formula and the generating function for these quaternions. Finally, we calculate Cassini, Catalan, Vajda and d’Ocagne identities for higher order Jacobsthal quaternions. © 2023, Gazi Universitesi. All rights reserved.
dc.identifier.doi10.35378/gujs.1002454
dc.identifier.eissn2147-1762
dc.identifier.endpage347
dc.identifier.issn2147-1762
dc.identifier.issue1
dc.identifier.scopus2-s2.0-85150679258
dc.identifier.startpage336
dc.identifier.urihttps://rdlopen.rawdatalibrary.net/r/ebyu/12478
dc.identifier.volume36
dc.identifier.wosWOS:000979511700022
dc.language.isoen
dc.publisherGazi Universitesi
dc.relation.ispartofGazi University Journal of Science
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectBinet formula
dc.subjectExponential generating functions
dc.subjectHigher order Jacobsthal numbers
dc.subjectHigher order Jacobsthal quaternions
dc.subjectBinet formulas
dc.subjectHigh order jacobsthal number
dc.subjectHigh order jacobsthal quaternion
dc.subjectHigh-order
dc.subjectHigher-order
dc.subjectJacobsthal numbers
dc.subjectRecurrence relations
dc.titleOn Quaternions with Higher Order Jacobsthal Numbers Components
dc.typeArticle
dspace.entity.typePublication
rdl.citation.scopus15
rdl.citation.trdizin4
rdl.citation.wos7
rdl.departmentERZİNCAN BİNALİ YILDIRIM ÜNİVERSİTESİ
rdl.oa.statusgold
rdl.source.indexSCOPUS
rdl.source.indexWOS
rdl.source.indexTRDIZIN
rdl.wos.indexEmerging Sources Citation Index (ESCI)