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

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.