Open AccessHybrid Quaternions of Leonardo
Author(s) -
Milena Carolina Paz,
Francisco Régis Vieira Alves,
Paula Catarino
Publication year - 2022
Publication title -
trends in computational and applied mathematics
Language(s) - English
Resource type - Journals
ISSN - 2676-0029
DOI - 10.5540/tcam.2022.023.01.00051
Subject(s) - quaternion , fibonacci number , dual quaternion , mathematics , sequence (biology) , extension (predicate logic) , integer (computer science) , algebra over a field , computer science , pure mathematics , discrete mathematics , geometry , biology , programming language , genetics
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.