Engin Özkan, Merve Taştan and Ali Aydoğdu

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 24, 2018, Number 3, Pages 47–55

DOI: 10.7546/nntdm.2018.24.3.47-55

**Full paper (PDF, 206 Kb)**

## Details

### Authors and affiliations

Engin Özkan

*Department of Mathematics, University of Erzincan Binali Yıldırım
Faculty of Arts and Sciences, Yalnızbag Campus, 24100, Erzincan, Turkey*

Merve Taştan

*Department of Mathematics, University of Erzincan Binali Yıldırım
Faculty of Arts and Sciences, Yalnızbag Campus, 24100, Erzincan, Turkey*

Ali Aydoğdu

*Department of Mathematics, University of Beykent
Ayazaga Campus, Ayazaga-Maslak, Sarıyer, 34485, Istanbul, Turkey*

### Abstract

In the present study, we define new 2-Fibonacci polynomials by using terms of a new family of Fibonacci numbers given in [4]. We show that there is a relationship between the coefficient of the 2-Fibonacci polynomials and Pascal’s triangle. We give some identities of the 2-Fibonacci polynomials. Afterwards, we compare the polynomials with known Fibonacci polynomials. We also express 2-Fibonacci polynomials by the Fibonacci polynomials. Furthermore, we prove some theorems related to the polynomials. Also, we introduce the derivative of the 2-Fibonacci polynomials.

### Keywords

- Fibonacci numbers
- Fibonacci polynomials
- Generalized Fibonacci polynomials

### 2010 Mathematics Subject Classification

- 11B39

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## Related papers

Taştan, M. & Özkan, E. (2021). Catalan transform of the *k*-Pell, *k*-Pell–Lucas and modified *k*-Pell sequence. *Notes on Number Theory and Discrete Mathematics*, 27(1), 198-207.

## Cite this paper

Özkan, E., Taştan, M., & Aydoğdu, A. (2018). 2-Fibonacci polynomials in the family of Fibonacci numbers. *Notes on Number Theory and Discrete Mathematics*, 24(3), 47-55, DOI: 10.7546/nntdm.2018.24.3.47-55.