On Quaternions with Higher Order Jacobsthal Numbers Components

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Gazi University Journal of Science
Volume:36 Issue:1
On Quaternions with Higher Order Jacobsthal Numbers Components

On Quaternions with Higher Order Jacobsthal Numbers Components

Authors : Engin ÖZKAN, Mine UYSAL

Pages : 336-347

Doi:10.35378/gujs.1002454

View : 18 | Download : 14

Publication Date : 2023-03-01

Article Type : Research Paper

Abstract :In this study, we present higher order Jacobsthal numbers. Then we define higher order Jacobsthal quaternions by using higher order Jacobsthal numbers. We give the concept of the norm and conjugate for these quaternions. We express and prove some propositions related to these quaternions. Also, we find the recurrence relation, the Binet formula and the generating function for these quaternions. Finally, we calculate Cassini, Catalan, Vajda and d’Ocagne identities for higher order Jacobsthal quaternions.
Keywords : Exponential generating functions, Higher order Jacobsthal numbers, Higher order Jacobsthal quaternions, Binet formula

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