On Quaternion-Gaussian Fibonacci Numbers and Their Properties-Reference-Cited by-同舟云学术

On Quaternion-Gaussian Fibonacci Numbers and Their Properties

Published:2021-03-01 Issue:1 Volume:29 Page:71-82
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Halici Serpil¹,Cerda-Morales Gamaliel²

Affiliation:

1. Pamukkale University , Faculty of Arts and Sciences, Department of Mathematics , Denizli / Turkey .

2. Instituto de Matemáticas , Pontificia Universidad Católica de Valparaíso , Blanco Viel 596, Valparaíso / Chile .

Abstract

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.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2021-0005

Reference14 articles.

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2. [2] Berzsenyi, G.: Gaussian Fibonacci numbers, The Fibonacci Quarterly 15(3) (1977), 233–236.

3. [3] Cerda-Morales, G.: Identities for Third Order Jacobsthal Quaternions. Adv. Appl. Clifford Algebr. 27(2) (2017), 1043–1053,10.1007/s00006-016-0654-1

4. [4] Cerda-Morales, G.: A note on dual third-order Jacobsthal vectors, Annales Mathematicae et Informaticae 52 (2020), 57–70.

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