Some results on Horadam quaternions

TAN E., Leung H.

CHAOS SOLITONS & FRACTALS, cilt.138, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 138
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1016/j.chaos.2020.109961
  • Dergi Adı: CHAOS SOLITONS & FRACTALS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, INSPEC, zbMATH
  • Anahtar Kelimeler: Quaternions, Fibonacci quaternions, Horadam quaternions, Matrix method, FIBONACCI, IDENTITIES, MATRIX
  • Ankara Üniversitesi Adresli: Evet

Özet

In this work, we present some matrix representations associated with the Horadam quaternions which are defined by W-n = w(n) + w(n+1)i + w(n+2j)+ w(n+3)k, where the components are taken from the Horadam sequence {w(n)}. 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. (C) 2020 Elsevier Ltd. All rights reserved.