Search

In this paper, by using q-integers and higher-order generalized Fibonacci numbers, we define the higher-order generalized Fibonacci quaternions with q-integer components. We give some special cases of these newly established quaternions. This article examines q-calculus and quaternions together. We obtain a Binet-like formula, some new identities, a generating function, a recurrence relation, an exponential generating function, and sum properties of quaternions with quantum integer coefficients. In addition, we obtain some new identities for these types of quaternions by using three new special matrices. [ABSTRACT FROM AUTHOR]

We provide an explicit solution for the terms of the sequence (xn, k) defined by xn, k = xn-1, k - (-1)b(n-2)/kcxn-2, k, for n > 3, setting x1,k = 1 and x2,k = 0. Several particular examples are considered. [ABSTRACT FROM AUTHOR]