On 3-parameter quaternions with higher order generalized Fibonacci numbers components
Can Kizilates, Ismail Yusuf Kibar
article (Uluslararası, Hakemli) | Yazar(lar): Can Kizilates, Ismail Yusuf Kibar | Yıl: 2024 | Dergi/Kurum: JOURNAL OF ANALYSIS | İndeks: WOS.ESCI | DOI: 10.1007/s41478-024-00730-7 | Anahtar Kelimeler: Quaternions, Higher order generalized Fibonacci quaternions, Recurrence relation, Generating functions, Matrix represen
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.