Filomat 2017 Volume 31, Issue 18, Pages: 5567-5579
https://doi.org/10.2298/FIL1718567T
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A new approach to Jacobsthal quaternions
Torunbalcı-Aydın Fügen (Yildiz Technical University Faculty of Chemical and Metallurgical Engineering, Department of Mathematical Engineering Davutpasa Campus, Esenler, Istanbul, Turkey)
Yüce Salim (Yildiz Technical University Faculty of Arts and Sciences, Department of Mathematics Davutpasa Campus, Esenler, Istanbul, Turkey)
The Jacobsthal quaternions defined by Szynal-Liana and Wloch [35]. In this
paper, we defined some properties of Jacobsthal quaternions. Also, we
investigated the relations between the Jacobsthal quaternions which
connected with Jacobsthal and Jacobsthal-Lucas numbers. Furthermore, we gave
the Binet formulas and Cassini identities for these quaternions.
Keywords: Jacobsthal number, Jacobsthal-Lucas number, Jacobsthal quaternion, Jacobsthal-Lucas quaternion