On a new generalization of Fibonacci quaternions

Elif Tan, Semih Yilmaz and Murat Sahin

Chaos, Solitons & Fractals, 2016, vol. 82, issue C, 1-4

Abstract: In this paper, we present a new generalization of the Fibonacci quaternions that are emerged as a generalization of the best known quaternions in the literature, such as classical Fibonacci quaternions, Pell quaternions, k -Fibonacci quaternions. We give the generating function and the Binet formula for these quaternions. By using the Binet formula, we obtain some well-known results. Also, we correct some results in [3] and [4] which have been overlooked that the quaternion multiplication is non commutative.

Keywords: Fibonacci sequence; Generalized Fibonacci sequence; Recurrence relations; Quaternions (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:82:y:2016:i:c:p:1-4

DOI: 10.1016/j.chaos.2015.10.021

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