Sure Köme and Cahit Köme

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 26, 2020, Number 2, Pages 61—70

DOI: 10.7546/nntdm.2020.26.2.61-70

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## Details

### Authors and affiliations

Sure Köme

*Department of Mathematics, Nevşehir Hacı Bektaş Veli University, Turkey
*

Cahit Köme

*Department of Information Technology, Nevşehir Hacı Bektaş Veli University, Turkey
*

### Abstract

The purpose of this study is to obtain a new generalized quaternions sequences by using hyperbolic functions with second order recurrence sequences. First of all, we define the symmetrical second order hyperbolic sine and the symmetrical second order hyperbolic cosine quaternions. Then, we investigate norms and some relations between these type of quaternions. We also obtain generating functions, Binet formulas, Catalan’s identity, Cassini’s identity and d’Ocagne’s identity of second order hyperbolic quaternions sequences.

### Keywords

- Second order hyperbolic functions
- Quaternions
- Binet formula
- Generating function

### 2010 Mathematics Subject Classification

- 11B37
- 11R52
- 05A15
- 11B83

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## Cite this paper

Köme, S., & Köme, C. (2020). On the symmetrical second order hyperbolic quaternions sequences. Notes on Number Theory and Discrete Mathematics, 26 (2), 61-70, doi: 10.7546/nntdm.2020.26.2.61-70.