Dual-complex k-Pell quaternions

Fügen Torunbalcı Aydın
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 25, 2019, Number 3, Pages 111–125
DOI: 10.7546/nntdm.2019.25.3.111-125
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Fügen Torunbalcı Aydın
Department of Mathematical Engineering
Faculty of Chemical and Metallurgical Engineering
Yildiz Technical University
Davutpasa Campus, 34220, Esenler, Istanbul, Turkey

Abstract

In this paper, dual-complex k-Pell numbers and dual-complex k-Pell quaternions are defined. Also, some algebraic properties of dual-complex k-Pell numbers and quaternions which are connected with dual-complex numbers and k-Pell numbers are investigated. Furthermore, Honsberger Identity, d’Ocagne’s Identity, Binet’s Formula, Cassini’s Identity and Catalan’s Identity for these quaternions are given.

Keywords

• Dual number
• Dual-complex number
• k-Pell number
• Dual-complex k-Pell number
• k-Pell quaternion
• Dual-complex k-Pell quaternion

2010 Mathematics Subject Classification

• 11B37
• 20G20
• 11R52

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