Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers

Abstract

The aim of this paper is to research the structural properties of the Fibonacci polynomials and Fibonacci numbers and obtain some identities. To achieve this purpose, we first introduce a new second-order nonlinear recursive sequence. Then, we obtain our main results by using this new sequence, the properties of the power series, and the combinatorial methods.

Keywords

• Fibonacci polynomials
• Fibonacci numbers
• recursive sequence
• combinatorial method
• power series
• identity