A new perspective on Fibonacci and Lucas numbers

Değirmen N., Duyar C.

FILOMAT, vol.37, no.28, pp.9561-9574, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 28
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2328561d
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.9561-9574
  • Keywords: Binet’s formula, Fibonacci number, generating function, Lucas number, non-Newtonian calculus
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In the present work, we introduce a new version of Fibonacci and Lucas numbers which we will call non-Newtonian Fibonacci and non-Newtonian Lucas numbers. Also, we discuss a variety of some properties of them. Furthermore, we give some formulas and identities such as Binet's formula, the d'Ocagne's identity, Cassini's identity and Gelin-Cesaro identity involving these new types and we find the generating functions for these numbers.