2-Fibonacci polynomials in the family of Fibonacci numbers

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)

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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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