On New Spinor Sequences of Jacobsthal and Jacobsthal-Lucas Quaternions

Year 2024, Volume: 14 Issue: 1, 17 - 38, 28.06.2024

Tülay Erişir , Mehmet Ali Güngör

https://doi.org/10.37094/adyujsci.1464592

Abstract

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, sum formulas and generating functions of these spinor sequences, which are called as Jacobsthal and Jacobsthal-Lucas spinor sequences, are expressed. Then, the 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.

Keywords

Jacobsthal numbers, Jacobsthal-Lucas numbers, Quaternions, Spinors

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