A new perspective on Fibonacci and Lucas numbers
FILOMAT, cilt.37, sa.28, ss.9561-9574, 2023 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 37 Sayı: 28
- Basım Tarihi: 2023
- Doi Numarası: 10.2298/fil2328561d
- Dergi Adı: FILOMAT
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
- Sayfa Sayıları: ss.9561-9574
- Anahtar Kelimeler: Binet’s formula, Fibonacci number, generating function, Lucas number, non-Newtonian calculus
- Ondokuz Mayıs Üniversitesi Adresli: Evet
Özet
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.