Pauli–Fibonacci quaternions

Fügen Torunbalcı Aydın
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 27, 2021, Number 3, Pages 184–193
DOI: 10.7546/nntdm.2021.27.3.184-193
Full paper (PDF, 177 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

The aim of this work is to consider the Pauli–Fibonacci quaternions and to present some properties involving this sequence, including the Binet’s formula and generating functions. Furthermore, the Honsberger identity, the generating function, d’Ocagne’s identity, Cassini’s identity, Catalan’s identity for these quaternions are given. The matrix representations for Pauli–Fibonacci quaternions are introduced.

Keywords

• Pauli matrix
• Pauli quaternion
• Fibonacci number
• Fibonacci quaternion
• Pauli–Fibonacci quaternion

2020 Mathematics Subject Classification

• 11R52
• 20G20

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