Generalized k-Order Fibonacci Hybrid Quaternions

Year 2022, Volume: 15 Issue: 2, 670 - 683, 31.08.2022

Kübra Gül

https://doi.org/10.18185/erzifbed.1132164

Abstract

In this study, generalized k-order Fibonacci hybrid quaternion is defined. We give recurrence relation, generating function, the summation formula and some properties for these quaternions. Furthermore, the matrix representation for generalized k-order Fibonacci hybrid quaternions is determined. The Q_k matrix defined for k-order Fibonacci numbers is given for the generalized k-order Fibonacci hybrid quaternions. By the means of this matrix and another defined matrices, several identities of these quaternions are also obtained.

Keywords

Fibonacci sequence, k-order Fibonacci sequence, hybrid numbers, quaternions.

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