On Quaternions with Higher Order Jacobsthal Numbers Components
Engi̇n Özkan, Mi̇ne Uysal
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.
Topics & Concepts
QuaternionRecurrence relationMathematicsAlgebra over a fieldCombinatoricsArithmeticPure mathematicsGeometryAdvanced Mathematical Theories and ApplicationsBiofield Effects and Biophysics