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

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## Details

### 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

## Related papers

## Cite this paper

Özkan, E., & Uysal, M. (2022). On hyperbolic *k*-Jacobsthal and *k*-Jacobsthal–Lucas octonions. *Notes on Number Theory and Discrete Mathematics*, 28(2), 318-330, DOI: 10.7546/nntdm.2022.28.2.318-330.