On hyperbolic k-Jacobsthal and k-Jacobsthal–Lucas octonions

Engin Özkan and Mine Uysal
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 2, Pages 318–330
DOI: 10.7546/nntdm.2022.28.2.318-330
Full paper (PDF, 344 Kb)

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Authors and affiliations

Engin Özkan
Department of Mathematics, Faculty of Arts and Sciences,
Erzincan Binali Yıldırım University, Erzincan, Turkey

Mine Uysal
Graduate School of Natural and Applied Sciences,
Erzincan Binali Yıldırım University, Erzincan, Turkey

Abstract

In this work, we investigate the hyperbolic k-Jacobsthal and k-Jacobsthal–Lucas octonions. We give Binet’s Formula, Cassini’s identity, Catalan’s identity, d’Ocagne identity, generating functions of the hyperbolic k-Jacobsthal and k-Jacobsthal–Lucas octonions. Also, we present many properties of these octonions.

Keywords

• Hyperbolic k-Jacobsthal octonions
• Hyperbolic k-Jacobsthal–Lucas octonions
• Binet formula
• Cassini identity
• Catalan identity

2020 Mathematics Subject Classification

• 11B39
• 11B37

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Manuscript history

• Received: 2 February 2022
• Revised: 9 May 2022
• Accepted: 7 June 2022
• Online First: 10 June 2022