Pauli-Fibonacci quaternions

Abstract

The aim of this work is to consider the Pauli-Fibonacci quaternions and to present some properties involving this sequence, including the Binet's formula and generating functions. Furthermore, the Honsberger identity, the generating function, d'Ocagne's identity, Cassini's identity, Catalan's identity for these quaternions are given. The matrix representations for Pauli-Fibonacci quaternions are introduced.