Unrestricted Fibonacci and Lucas quaternions

Year 2021, Volume: 4 Issue: 1, 1 - 9, 01.03.2021

Ahmet Daşdemir Göksal Bilgici

https://doi.org/10.33401/fujma.752758

Abstract

Many quaternion numbers associated with Fibonacci and Lucas numbers or even their generalizations have been defined and widely discussed so far. In all the studies, the coefficients of these quaternions have been selected from consecutive terms of these numbers. In this study, we define other generalizations for the usual Fibonacci and Lucas quaternions. We also present some properties, including the Binet's formulas and d'Ocagne's identities, for these types of quaternions.

Keywords

Fibonacci quaternion, Lucas quaternion, Binet's formula, Catalan's identity, Generating function

Supporting Institution

Research Fund of Kastamonu University

Project Number

KÜBAP-01/2017-1

Thanks

The authors would like to declare the financial support provided by the Research Fund of Kastamonu University under project number KÜBAP-01/2017-1.

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