Hyper-Dual Leonardo Quaternions

Year 2024, Issue: 48, 78 - 89, 30.09.2024

Tülay Yağmur

https://doi.org/10.53570/jnt.1525070

Abstract

In this paper, hyper-dual Leonardo quaternions are defined and studied. Some basic properties of the hyper-dual Leonardo quaternions, including their relationships with the hyper-dual Fibonacci quaternions and hyper-dual Lucas quaternions, are analyzed. In addition, some formulae and identities, such as the recurrence relations, Binet's formula, generating functions, Vajda's identity, certain sum formulae, and some binomial-sum formulae, are investigated for hyper-dual Leonardo quaternions.

Keywords

Dual numbers, hyper-dual numbers, quaternions, Fibonacci numbers, Leonardo numbers

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