SPLIT DUAL JACOBSTHAL AND JACOBSTHAL-LUCAS QUATERNIONS

Abstract

Many researchs have been studied on quaternions since Hamilton introduced them to the literature in 1843. In our paper, we gave split dual Jacobsthal (SDJ) and split dual Jacobsthal-Lucas (SDJL) quaternions over the algebra H(μ,n) with the basis {1; e1; e2; e3}, where  μ,n ∈ Z. Binet like formulaes are obtained for these quaternions. Also, given Vajda identities for SDJ and SDJL quaternions.As a special case of Vajda identities, d'Ocagne's, Cassini's and Catalan's identities are represented.