Circular-hyperbolic Fibonacci quaternions

Fügen Torunbalcı Aydın
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 26, 2020, Number 2, Pages 167–176
DOI: 10.7546/nntdm.2020.26.2.167-176
Full paper (PDF, 194 Kb)

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Authors and affiliations

Fügen Torunbalcı Aydın
Yildiz Technical University, Faculty of Chemical and Metallurgical Engineering
Department of Mathematical Engineering
Davutpasa Campus, 34220, Esenler, Istanbul, Turkey

Abstract

In this paper, circular-hyperbolic Fibonacci numbers and quaternions are defined. Also, some algebraic properties of circular-hyperbolic Fibonacci numbers and quaternions which are connected with circular-hyperbolic numbers and Fibonacci numbers are investigated. Furthermore, Honsberger’s identity, the generating function, Binet’s formula, d’Ocagne’s identity, Cassini’s identity, and Catalan’s identity for these quaternions are given.

Keywords

• Fibonacci number
• Hyperbolic number
• Dual-hyperbolic number
• Circular-hyperbolic number
• Circular-hyperbolic Fibonacci number

2010 Mathematics Subject Classification

• 11B37
• 20G20
• 11R52

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