Some Special Identities for Jacobsthal and Jacobsthal-Lucas Generalized Octonions

Abstract

Summary: We study on Jacobsthal and Jacobsthal-Lucas generalized octonions over the algebra \(\mathbb{O}(a, b, c)\) where \(a\), \(b\) and \(c\) are real numbers. We present Binet formulas for these types of octonions. Furthermore, we give some well-known identities such as Catalan's, Cassini's, d'Ocagne's identities and other special identities for Jacobsthal and Jacobsthal-Lucas generalized octonions.