Open Accessk-ORDER FIBONACCI QUATERNIONS
Author(s) -
Mustafa Aşçı,
Süleyman Aydınyüz
Publication year - 2021
Publication title -
journal of science and arts
Language(s) - English
Resource type - Journals
eISSN - 2068-3049
pISSN - 1844-9581
DOI - 10.46939/j.sci.arts-21.1-a04
Subject(s) - quaternion , fibonacci number , mathematics , fibonacci polynomials , matrix representation , order (exchange) , generalization , algebra over a field , combinatorics , pure mathematics , mathematical analysis , physics , geometry , group (periodic table) , finance , quantum mechanics , economics , orthogonal polynomials , difference polynomials
In this paper, we define and study another interesting generalization of the Fibonacci quaternions is called k-order Fibonacci quaternions. Then we obtain for Fibonacci quaternions, for Tribonacci quaternions and for Tetranacci quaternions. We give generating function, the summation formula and some properties about k-order Fibonacci quaternions. Also, we identify and prove the matrix representation for k-order Fibonacci quaternions. The matrix given for k-order Fibonacci numbers is defined for k-order Fibonacci quaternions and after the matrices with the k-order Fibonacci quaternions is obtained with help of auxiliary matrices, important relationships and identities are established.