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
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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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Cite this paper

Torunbalcı Aydın, F. (2020). Circular-hyperbolic Fibonacci quaternions. Notes on Number Theory and Discrete Mathematics, 26 (2), 167-176, doi: 10.7546/nntdm.2020.26.2.167-176.

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