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On 3-parameter quaternions with higher order generalized Fibonacci numbers components

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Abstract

In this article, 3-parameter higher order quaternions are introduced with the help of higher-order generalized Fibonacci quaternions and 3-parameter quaternions. This definition includes not only one-parameter, two and three-parameter quaternions, but also split quaternions, semi quaternions, and 1/4 quaternions. Moreover, some properties of quaternions such as conjugate, norm, recurrence relation, a generating function, an exponential generating function, and Vajda’s identity are examined. Finally, as an application by using the tridiagonal matrix whose entries are the higher order generalized Fibonacci 3-parameter quaternions, we obtain its determinants by means of the Chebyshev polynomials of the second kind.

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Authors and Affiliations

  1. Department of Mathematics, Zonguldak Bulent Ecevit University, Zonguldak, 67100, Turkey

    Can Kızılateş & İsmail Yusuf Kibar

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  1. Can Kızılateş
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  2. İsmail Yusuf Kibar
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All authors contributed equally to the manuscript and typed, read, and approved the final manuscript.

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Correspondence to Can Kızılateş.

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Communicated by S. Ponnusamy.

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Kızılateş, C., Kibar, İ.Y. On 3-parameter quaternions with higher order generalized Fibonacci numbers components. J Anal 32, 1819–1832 (2024). https://doi.org/10.1007/s41478-024-00730-7

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