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Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers [PDF]

Mathematics, 2018
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 ...
Wenpeng Zhang, Yuankui Ma
exaly   +4 more sources

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Fibonacci, Chebyshev, and Orthogonal Polynomials

The American Mathematical Monthly, 2005
(2005). Fibonacci, Chebyshev, and Orthogonal Polynomials. The American Mathematical Monthly: Vol. 112, No. 7, pp. 612-630.
Dov Aharonov, Alan F. Beardon, Kathy Driver   +2 more
openaire   +2 more sources

On Certain Properties of Parametric Kinds of Apostol-Type Frobenius–Euler–Fibonacci Polynomials

Axioms
This paper presents an overview of cosine and sine Apostol-type Frobenius–Euler–Fibonacci polynomials, as well as several identities that are associated with these polynomials.
Cheon-Seoung Ryoo, Waseem Ahmad Khan, Can Kizilateş   +2 more
exaly   +2 more sources

Polynomial Fibonacci–Hessenberg matrices

Chaos, Solitons & Fractals, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Esmaeili, Morteza, Esmaeili, Mostafa
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The Irregularity Polynomials of Fibonacci and Lucas cubes

Bulletin of the Malaysian Mathematical Sciences Society, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ömer Eğecioğlu, Elif Saygı, Zülfükar Saygı   +2 more
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Fibonacci Polynomials their Properties and Applications

Zeitschrift für Analysis und ihre Anwendungen, 1996
The paper deals with polynomials characterized by coefficients determined by successive elements of the Fibonacci sequence. Basic properties and applications of the Fibonacci polynomials are demonstrated. The index of concentration of Fibonacci polynomials at k
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ON SUMS OF BIVARIATE FIBONACCI POLYNOMIALS AND BIVARIATE LUCAS POLYNOMIALS

South East Asian J. of Mathematics and Mathematical Sciences, 2022
In this paper, we present the sum of s+1 consecutive member of Bivariate Fibonacci Polynomials and Bivariate Lucas Polynomials and related identities consisting even and odd terms. We present its two cross two matrix and find interesting properties such as nth power of the matrix.
Panwar, Yashwant K., Mansuri, Akhlak, Bhandari, Jaya   +2 more
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Supersymmetric Fibonacci polynomials

Analysis and Mathematical Physics, 2021
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Fibonacci and Lucas polynomials

Mathematical Proceedings of the Cambridge Philosophical Society, 1981
The Fibonacci and Lucas polynomials Fn(z) and Ln(z) are denned. These reduce to the familiar Fibonacci and Lucas numbers when z = 1. The polynomials are shown to satisfy a second order linear difference equation. Generating functions are derived, and also various simple identities, and relations with hypergeometric functions, Gegenbauer and Chebyshev ...
Doman, B. G. S., Williams, J. K.
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Some polynomials related to the Fibonacci polynomials

Bull. EATCS, 1994
In an earlier paper the author analyzed an algorithm to construct ``Fibonacci partitions of a set''. The polynomials involved are closely related to the Fibonacci polynomials. The sum \[ \sum_{1\leq k< n} (k)_ s \left( \begin{smallmatrix} n-1-k\\ k-1\end{smallmatrix} \right) x^ k (x- 1)^{n-2k}+ \sum_{0\leq ...
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