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Open AccessArticle

Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers

by Yuankui Ma 1 and Wenpeng Zhang 1,2,*
1
School of Science, Xi’an Technological University, Xi’an 710021, China
2
School of Mathematics, Northwest University, Xi’an 710127, China
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 334; https://doi.org/10.3390/math6120334
Received: 21 November 2018 / Revised: 15 December 2018 / Accepted: 16 December 2018 / Published: 18 December 2018
(This article belongs to the Special Issue Special Polynomials)
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. View Full-Text
Keywords: Fibonacci polynomials; Fibonacci numbers; recursive sequence; combinatorial method; power series; identity Fibonacci polynomials; Fibonacci numbers; recursive sequence; combinatorial method; power series; identity
MDPI and ACS Style

Ma, Y.; Zhang, W. Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers. Mathematics 2018, 6, 334.

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