<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept gaussian Fibonacci numbers as coefficients. Using the Binet form we prove fundamental relations between these numbers. Moreover, we investigate whether the quaternions newly defined provide existing some important identities such as Cassini’s identity for quaternions.</p></abstract>

We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept gaussian Fibonacci numbers as coefficients. Using the Binet form we prove fundamental relations between these numbers. Moreover, we investigate whether the quaternions newly defined provide existing some important identities such as Cassini’s identity for quaternions.

On Quaternion-Gaussian Fibonacci Numbers and Their Properties

Faculty of Arts and Sciences, Department of Mathematics

Pontificia Universidad Católica de Valparaíso

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On Quaternion-Gaussian Fibonacci Numbers and Their Properties"}

We study properties of Gaussian Fibonacci numbers. We start with some basic identities. Thereafter, we focus on properties of the quaternions that accept...

On Quaternion-Gaussian Fibonacci Numbers and Their Properties

Published Online: Apr 13, 2021

Page range: 71 - 82

Received: Mar 17, 2020

Accepted: May 01, 2020

DOI: https://doi.org/10.2478/auom-2021-0005

Keywords
Fibonacci number, gaussian number, quaternion, recurrence relation

© 2021 Serpil Halici et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On Quaternion-Gaussian Fibonacci Numbers and Their Properties

Published Online: Apr 13, 2021

Page range: 71 - 82

Received: Mar 17, 2020

Accepted: May 01, 2020

DOI: https://doi.org/10.2478/auom-2021-0005

KeywordsFibonacci number, gaussian number, quaternion, recurrence relation

© 2021 Serpil Halici et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Fibonacci number, gaussian number, quaternion, recurrence relation