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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Kapsamı
Uluslararası
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Type
Hakemli
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Index info
WOS.ESCI
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Language
English
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Article Type
None
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Keywords
Quaternions Higher order generalized Fibonacci quaternions Recurrence relation Generating functions Matrix representation Determinant