Geodesic
A new perspective on Fibonacci and Lucas numbers
Filomat, Tome 37 (2023) no. 28, p. 9561

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

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-Cesàro identity involving these new types and we find the generating functions for these numbers.
DOI : 10.2298/FIL2328561D
Classification : 11B39, 11B83, 05A15, 11U10
Keywords: non-Newtonian calculus, Lucas number, Fibonacci number, Binet’s formula, generating function 
Nilay Değirmen; Cenap Duyar. A new perspective on Fibonacci and Lucas numbers. Filomat, Tome 37 (2023) no. 28, p. 9561 . doi: 10.2298/FIL2328561D
@article{10_2298_FIL2328561D,
     author = {Nilay De\u{g}irmen and Cenap Duyar},
     title = {A new perspective on {Fibonacci} and {Lucas} numbers},
     journal = {Filomat},
     pages = {9561 },
     year = {2023},
     volume = {37},
     number = {28},
     doi = {10.2298/FIL2328561D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2328561D/}
}
TY  - JOUR
AU  - Nilay Değirmen
AU  - Cenap Duyar
TI  - A new perspective on Fibonacci and Lucas numbers
JO  - Filomat
PY  - 2023
SP  - 9561 
VL  - 37
IS  - 28
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2328561D/
DO  - 10.2298/FIL2328561D
LA  - en
ID  - 10_2298_FIL2328561D
ER  - 
%0 Journal Article
%A Nilay Değirmen
%A Cenap Duyar
%T A new perspective on Fibonacci and Lucas numbers
%J Filomat
%D 2023
%P 9561 
%V 37
%N 28
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2328561D/
%R 10.2298/FIL2328561D
%G en
%F 10_2298_FIL2328561D

Cité par Sources :