Honam Mathematical Journal (호남수학학술지)

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INVESTIGATING THE DUAL QUATERNION EXTENSION OF THE 𝓓𝓖𝓒 LEONARDO SEQUENCE

  • Cigdem Zeynep Yilmaz (Department of Mathematics, Istanbul Bilgi University) ;
  • Gulsum Yeliz Sacli (Department of Mathematics, Yildiz Technical University)
  • Received : 2024.07.02
  • Accepted : 2024.08.05
  • Published : 2024.12.20
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Abstract

In this study, we introduce a new generalization of the Leonardo sequence, dual quaternions with the 𝓓𝓖𝓒 Leonardo sequence coefficients, depending on the parameter p ∈ ℝ. This generalization gives dual quaternions with the dual-complex Leonardo sequence for 𝖕 = -1, dual quaternions with the hyper-dual Leonardo sequence for 𝖕 = 0, and dual quaternions with the dual-hyperbolic Leonardo sequence for 𝖕 = 1. The basic algebraic structures and some special characteristic relations are presented, as well as the Binet's formula, generating function, d'Ocagne's, Catalan's, Cassini's, and Tagiuri's identities.

Keywords

Acknowledgement

This work has been supported by TUBITAK BIDEB 2209-A Research Project Support Programme for Undergraduate Students 2022 1st Term (The Scientific and Technological Research Council of Turkiye-Directorate of Science Fellowships and Grant Programmes) under support number 1919B012203959.

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