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, vol.40, no.1, pp.179-187, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.14744/sigma.2022.00014
  • Journal Name: Sigma Journal of Engineering and Natural Sciences
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Page Numbers: pp.179-187
  • Keywords: Dual-generalized complex numbers, Fibonacci numbers, Lucas numbers MSC 2010, 11B39, 11B83
  • Yıldız Technical University Affiliated: Yes

Abstract

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.