On New Spinor Sequences of Jacobsthal and Jacobsthal-Lucas Quaternions; [Jacobsthal ve Jacobsthal-Lucas Kuaterniyonlarının Yeni Spinor Dizileri Üzerine]

In this study, two new spinor sequences using spinor representations of Jacobsthal and Jacobsthal-Lucas quaternions are defined. Moreover, some formulas such that Binet, Cassini, summation formulas and generating functions of these spinor sequences, which are called as Jacobsthal and Jacobsthal-Lucas spinor sequences, are expressed. Then, some relationships between Jacobsthal and Jacobsthal-Lucas spinors are obtained. Therefore, an easier and more interesting representation of Jacobsthal and Jacobsthal-Lucas quaternions, which are generalization of Jacobsthal and Jacobsthal-Lucas number sequences, are obtained. We believe that these new spinor sequences will be useful and advantageable in many branches of science, such as geometry, algebra and physics. © 2024, Adiyaman University. All rights reserved.