The generalized bi-periodic Fibonacci quaternions and octonions

Abstract

In this paper, we present a further generalization of the biperiodic Fibonacci quaternions and octonions. We give the generating function, the Binet formula, and some basic properties of these quaternions and octonions. The results of this paper not only give a generalization of the bi-periodic Fibonacci quaternions and octonions, but also include new results such as the matrix representation and the norm value of the generalized bi-periodic Fibonacci quaternions.2000 Mathematics Subject Classification. 11B39, 05A15, 11R52.

More Identities for Fibonacci and Lucas quaternions

“…The …rst type Cassini identity for the generalized bi-periodic Fibonacci quaternions was given by Tan et. al [10].…”

Hyper-dual Horadam quaternions

“…These numbers can also be seen as dual numbers with Fibonacci quaternion coefficients. A generalization of dual Fibonacci quaternions can be found in [18]. In [13], the author introduced the dual Horadam quaternions as…”