On Quaternions with Higher Order Jacobsthal Numbers Components

Year 2023, Volume: 36 Issue: 1, 336 - 347, 01.03.2023

Engin Özkan , Mine Uysal

https://doi.org/10.35378/gujs.1002454

Cited By: 4

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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