On some identities for the DGC Leonardo sequence

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dc.authoridSaçlı (Şentürk), Gülsüm Yeliz/0000-0002-8647-1801
dc.contributor.authorYılmaz, Ciğdem Zeynep
dc.contributor.authorSaçlı, Gülsüm Yeliz
dc.date.accessioned2024-09-11T19:53:29Z
dc.date.available2024-09-11T19:53:29Z
dc.date.issued2024
dc.departmentİstanbul Gelişim Üniversitesien_US
dc.description.abstractIn this study, we examine the Leonardo sequence with dual-generalized complex (DGC) coefficients for p is an element of R. Firstly, we express some summation formulas related to the DGC Fibonacci, DGC Lucas, and DGC Leonardo sequences. Secondly, we present some order-2 characteristic relations, involving d'Ocagne's, Catalan's, Cassini's, and Tagiuri's identities. The essential point of the paper is that one can reduce the calculations of the DGC Leonardo sequence by considering p. This generalization gives the dual-complex Leonardo sequence for p = -1, hyper-dual Leonardo sequence for p = 0, and dual-hyperbolic Leonardo sequence for p = 1.en_US
dc.description.sponsorshipTUBITAK BIDEB 2209-A University Students Research Projects Support Program 2022 1st Term (The Scientific and Technological Research Council of Turkey-Directorate of Science Fellowships and Grant Programmes) [1919B012203959]en_US
dc.description.sponsorshipThis work has been supported by TUBITAK BIDEB 2209-A University Students Research Projects Support Program 2022 1st Term (The Scientific and Technological Research Council of Turkey-Directorate of Science Fellowships and Grant Programmes) under support number 1919B012203959.en_US
dc.identifier.doi10.7546/nntdm.2024.30.2.253-270
dc.identifier.endpage270en_US
dc.identifier.issn1310-5132
dc.identifier.issn2367-8275
dc.identifier.issue2en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.startpage253en_US
dc.identifier.urihttps://doi.org/10.7546/nntdm.2024.30.2.253-270
dc.identifier.urihttps://hdl.handle.net/11363/8143
dc.identifier.volume30en_US
dc.identifier.wosWOS:001247880700004en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherBulgarian Acad Scienceen_US
dc.relation.ispartofNotes on Number Theory And Discrete Mathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.snmz20240903_Gen_US
dc.subjectBinet's formulaen_US
dc.subjectLeonardo numbersen_US
dc.subjectDual -generalized complex numbers.en_US
dc.titleOn some identities for the DGC Leonardo sequenceen_US
dc.typeArticleen_US

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