On Dual Quaternions with $k-$Generalized Leonardo Components
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 inv...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Naim Çağman
2023-09-01
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| Series: | Journal of New Theory |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/3269358 |
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| Summary: | 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. |
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| ISSN: | 2149-1402 |