A note on bi-periodic Fibonacci and Lucas quaternions

TAN E., YILMAZ S., ŞAHİN M.

CHAOS SOLITONS & FRACTALS, cilt.85, ss.138-142, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 85
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.chaos.2016.01.025
  • Dergi Adı: CHAOS SOLITONS & FRACTALS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.138-142
  • Anahtar Kelimeler: Lucas sequence, Generalized Lucas sequence, Recurrence relations, Quaternions
  • Ankara Üniversitesi Adresli: Evet

Özet

Motivated by the our recent work in Tan et al., 2016, related to the bi-periodic Fibonacci quaternions, here we introduce the bi-periodic Lucas quaternions that gives the Lucas quaternions as a special case. We give the generating function and the Binet formula for these quaternions. Also, we give the relationships between bi-periodic Fibonacci quaternions and bi-periodic Lucas quaternions. (C) 2016 Elsevier Ltd. All rights reserved.