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      Hybrid Quaternions of Leonardo

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          Abstract

          ABSTRACT In this article, we intend to investigate the Leonardo sequence presenting the hybrid Leonardo quaternions. To explore Hybrid Quaternions of Leonardo, the priori, sequence of Leonardo, quaternions and hybrid numbers were presented. Soon after, its recurrence, characteristic equation, its relation with the Fibonacci quaternions, generating function, Binet’s formula, as well as its extension to non-positive integer indices were developed. Finally, identities involving Leonardo’s hybrid quaternions are presented.

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          Most cited references25

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          On Fibonacci Quaternions

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            Complex Fibonacci Numbers and Fibonacci Quaternions

            A. Horadam (1963)
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              On Complex Fibonacci Quaternions

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                Author and article information

                Journal
                tcam
                Trends in Computational and Applied Mathematics
                Trends Comput. Appl. Math.
                Sociedade Brasileira de Matemática Aplicada e Computacional - SBMAC (São Carlos, SP, Brazil )
                2676-0029
                January 2022
                : 23
                : 1
                : 51-62
                Affiliations
                [3] orgnameUniversity of Trás-os-Montes orgdiv1Department of Mathematics Portugal pcatarino23@ 123456gmail.com
                [2] Fortaleza CE orgnameFederal Institute of Education, Science, Technology of Ceará orgdiv1Department of Mathematics Brazil fregis@ 123456ifce.edu.br
                [1] Fortaleza CE orgnameFederal Institute of Education, Science, Technology of Ceará orgdiv1Department of Mathematics Brazil milenacarolina24@ 123456gmail.com
                Article
                S2676-00292022000100051 S2676-0029(22)02300100051
                10.5540/tcam.2022.023.01.00051
                870d3398-b070-40cc-90e5-b5c2481d2e43

                This work is licensed under a Creative Commons Attribution 4.0 International License.

                History
                : 20 April 2021
                : 18 June 2021
                Page count
                Figures: 0, Tables: 0, Equations: 0, References: 25, Pages: 12
                Product

                SciELO Brazil

                Categories
                Articles

                Leonardo sequence,hybrid numbers,hybrid Leonardo quaternions

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