A comprehensive survey of dual-generalized complex Fibonacci and Lucas numbers

GÜRSES N., ŞENTÜRK G. Y., YÜCE S.

Sigma Journal of Engineering and Natural Sciences, cilt.40, sa.1, ss.179-187, 2022 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.14744/sigma.2022.00014
  • Dergi Adı: Sigma Journal of Engineering and Natural Sciences
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Sayfa Sayıları: ss.179-187
  • Anahtar Kelimeler: Dual-generalized complex numbers, Fibonacci numbers, Lucas numbers MSC 2010, 11B39, 11B83
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

This paper aims to develop dual-generalized complex Fibonacci and Lucas numbers and obtain recurrence relations. Fibonacci and Lucas’s approach to dual-generalized complex numbers contains dual-complex, hyper-dual and dual-hyperbolic situations as special cases and allows general contributions to the literature for all real number p. For this purpose, Binet’s formulas along with Tagiuri’s, Hornsberger’s, D’Ocagne’s, Cassini’s and Catalan’s identities, are calculated for dual-generalized complex Fibonacci and Lucas numbers. Finally, the results are given, and the special cases for this unification are classified.