Some results on Horadam quaternions

Elif Tan and Ho-Hon Leung

Chaos, Solitons & Fractals, 2020, vol. 138, issue C

Abstract: In this work, we present some matrix representations associated with the Horadam quaternions which are defined by Wn=wn+wn+1i+wn+2j+wn+3k, where the components are taken from the Horadam sequence {wn}. We derive many identities related to them by using the matrix technique which is more practical. Since various well-known Fibonacci-type quaternion matrices are special cases of Horadam quaternion matrices, we have a unified way of dealing with many special quaternion sequences in the literature. As an application, we derive some binomial-sum identities.

Keywords: Quaternions; Fibonacci quaternions; Horadam quaternions; Matrix method (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:138:y:2020:i:c:s096007792030360x

DOI: 10.1016/j.chaos.2020.109961

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