New families of Fibonacci and Lucas octonions with $$Q-$$ Q - integer components

Can Kızılateş () and Emrah Polatlı ()
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Can Kızılateş: Zonguldak Bülent Ecevit University
Emrah Polatlı: Zonguldak Bülent Ecevit University

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 1, 231-240

Abstract: Abstract A number of families of quaternion and octonion number sequence such as (Fibonacci quaternion, Fibonacci octonion and so forth) have been studied by several authors in many different ways. Besides, several formulas and identities involving these number sequences have been presented. The aim of this paper is to consider the octonions with components including quantum integers. We called these type of octonions the $$q-$$ q - Fibonacci octonions and the $$q-$$ q - Lucas octonions respectively. Furthermore, we give Binet formulas, exponential generating functions, summation formulas, Catalan identities, Cassini identities and d’Ocagne identities, respectively.

Keywords: Octonions; Horadam numbers; $$Q-$$ Q - integer; $$Q-$$ Q - calculus; 11B39; 11R52; 05A15 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00073-0

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