Hybrid Quaternions of Leonardo

Abstract

In this article, we intend to investigate the Leonardo sequence presenting the hybrid Leonardo quaternions. To explore Hybrid Quaternions of Leonardo, the priori, sequence of Leonardo,
quaternions and hybrid numbers were presented. Soon after, its recurrence, characteristic equation, its relation with the Fibonacci quaternions, generating function, Binet’s formula, as well as its extension to non-positive integer indices were developed. Finally, identities involving Leonardo’s hybrid quaternions are presented.