호남수학학술지 (Honam Mathematical Journal)

  • 제46권4호
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  • Pages.677-696
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  • 2024
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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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)
  • 투고 : 2024.07.02
  • 심사 : 2024.08.05
  • 발행 : 2024.12.20
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초록

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.

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과제정보

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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