On Dual Quaternions with k−Generalized Leonardo Components


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YILMAZ Ç. Z., ŞENTÜRK G. Y.

Journal of New Theory, no.44, pp.31-42, 2023 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.53570/jnt.1328605
  • Journal Name: Journal of New Theory
  • Journal Indexes: TR DİZİN (ULAKBİM)
  • Page Numbers: pp.31-42
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, we define a one-parameter generalization of Leonardo dual quaternions, namely $k-$generalized Leonardo-like dual quaternions. We introduce the properties of $k$-generalized Leonardo-like dual quaternions, including relations with Leonardo, Fibonacci, and Lucas dual quaternions. We investigate their characteristic relations, involving the Binet-like formula, the generating function, the summation formula, Catalan-like, Cassini-like, d'Ocagne-like, Tagiuri-like, and Hornsberger-like identities. The crucial part of the present paper is that one can reduce the calculations of Leonardo-like dual quaternions by considering $k$. For $k=1$, these results are generalizations of the ones for ordered Leonardo quadruple numbers. Finally, we discuss the need for further research.