k-Fibonacci Polynomials in The Family of Fibonacci Numbers

Abstract

Abstract: In this study, we define k-Fibonacci Polynomials by using terms of a new family of Fibonacci numbers given by Mikkawy and Sogabe. We compare the polynomials with known Fibonacci polynomial. Furthermore, we show the relationship between Pascal’s triangle and the coefficient of the k-Fibonacci polynomials. We give some important properties of the polynomial.

2010 Mathematics Subject Classification: 11B39.

Keywords: Fibonacci Numbers, Fibonacci Polynomials, Pascal’s triangle, k-Fibonacci polynomials, The derivative of the k-Fibonacci polynomial

Cite this Article: Engin Özkan, Merve Taştan, k-Fibonacci Polynomials in The Family of Fibonacci Numbers. Research & Reviews: Discrete Mathematical Structures. 2019; 6(3): 19–22p.