SPLIT DUAL JACOBSTHAL AND JACOBSTHAL-LUCAS QUATERNIONS

UMIT TOKESER *

Department of Mathematics, Faculty of Science, Kastamonu University, Kastamonu 37100, Turkey.

ZAFER UNAL

Department of Mathematics, Faculty of Science, Kastamonu University, Kastamonu 37100, Turkey.

*Author to whom correspondence should be addressed.


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.

Keywords: quaternions, dual Jacobsthal and dual Jacobsthal-Lucas numbers, plit dual Jacobsthal and split dual Jacobsthal-Lucas quaternions


How to Cite

TOKESER, U., & UNAL, Z. (2022). SPLIT DUAL JACOBSTHAL AND JACOBSTHAL-LUCAS QUATERNIONS. Asian Journal of Mathematics and Computer Research, 29(3), 1–9. https://doi.org/10.56557/ajomcor/2022/v29i37938

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