On the symmetrical second order hyperbolic quaternions sequences

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
Full paper (PDF, 164 Kb)

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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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