On a new generalization of Fibonacci quaternions

TAN E., YILMAZ S., Sahina M.

CHAOS SOLITONS & FRACTALS, cilt.82, ss.1-4, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 82
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.chaos.2015.10.021
  • Dergi Adı: CHAOS SOLITONS & FRACTALS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1-4
  • Anahtar Kelimeler: Fibonacci sequence, Generalized Fibonacci sequence, Recurrence relations, Quaternions
  • Ankara Üniversitesi Adresli: Evet

Özet

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 Billet 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. (C) 2015 Elsevier Ltd. All rights reserved.