scholarly journals Some New Identities for the Generalized Fibonacci Polynomials by the Q(x) Matrix

2021 ◽  
Vol 13 (2) ◽  
pp. 21
Author(s):  
Chung-Chuan Chen ◽  
Lin-Ling Huang
Keyword(s):  
Fibonacci Polynomials ◽  
New Approach ◽  
Lucas Polynomials ◽  
Type Formula ◽  
Type Identity ◽  
Fibonacci Polynomial

We obtain some new identities for the generalized Fibonacci polynomial by a new approach, namely, the Q(x) matrix. These identities including the Cassini type identity and Honsberger type formula can be applied to some polynomial sequences such as Fibonacci polynomials, Lucas polynomials, Pell polynomials, Pell-Lucas polynomials and so on, which generalize the previous results in references.

scholarly journals HOMFLY Polynomials of Torus Links as Generalized Fibonacci Polynomials

10.37236/5324 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Kemal Taşköprü ◽  
İsmet Altıntaş
Keyword(s):  
Homfly Polynomial ◽  
Matrix Representations ◽  
Fibonacci Polynomials ◽  
Lucas Polynomials ◽  
Fundamental Properties ◽  
Conway Polynomial ◽  
The Matrix ◽  
Fibonacci Polynomial ◽  
Homfly Polynomials ◽  
Torus Links

The focus of this paper is to study the HOMFLY polynomial of $(2,n)$-torus link as a generalized Fibonacci polynomial. For this purpose, we first introduce a form of generalized Fibonacci and Lucas polynomials and provide their some fundamental properties. We define the HOMFLY polynomial of $ (2,n) $-torus link with a way similar to our generalized Fibonacci polynomials and provide its fundamental properties. We also show that the HOMFLY polynomial of $ (2,n) $-torus link can be obtained from its Alexander-Conway polynomial or the classical Fibonacci polynomial. We finally give the matrix representations and prove important identities, which are similar to the Fibonacci identities, for the our generalized Fibonacci polynomial and the HOMFLY polynomial of $ (2,n) $-torus link.

scholarly journals Some Properties of the(p,q)-Fibonacci and(p,q)-Lucas Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
GwangYeon Lee ◽  
Mustafa Asci
Keyword(s):  
Generating Functions ◽  
Combinatorial Identities ◽  
Fibonacci Polynomials ◽  
Lucas Polynomials ◽  
Pascal Matrix ◽  
Riordan Arrays ◽  
Combinatorial Sums

Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper we consider the Pascal matrix and define a new generalization of Fibonacci polynomials called(p,q)-Fibonacci polynomials. We obtain combinatorial identities and by using Riordan method we get factorizations of Pascal matrix involving(p,q)-Fibonacci polynomials.

On Gauss Fibonacci polynomials, on Gauss Lucas polynomials and their applications

2019 ◽  
Vol 48 (3) ◽  
pp. 952-960 ◽  
Author(s):  
Engin Özkan ◽  
Merve Taştan
Keyword(s):  
Fibonacci Polynomials ◽  
Lucas Polynomials

High rates of Fibonacci polynomials coding theory

2014 ◽  
Vol 06 (04) ◽  
pp. 1450053
Author(s):  
Bandhu Prasad
Keyword(s):  
Coding Theory ◽  
Fibonacci Polynomials ◽  
New Class ◽  
Matrix Formula ◽  
Fibonacci Polynomial ◽  
Square Matrix

In this paper, a new class of square matrix [Formula: see text] of order pm is introduced, where (p = 3, 4, 5, …), (m = 1, 2, 3, …) and for integers n, x ≥ 1. Fibonacci polynomial coding and decoding methods are followed from [Formula: see text] matrix and high code rates are obtained.

Infinite sums for Fibonacci polynomials and Lucas polynomials

2018 ◽  
Vol 50 (3) ◽  
pp. 621-637
Author(s):  
Bing He ◽  
Ruiming Zhang
Keyword(s):  
Fibonacci Polynomials ◽  
Lucas Polynomials ◽  
Infinite Sums

scholarly journals A Closed Formula for the Horadam Polynomials in Terms of a Tridiagonal Determinant

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 782 ◽  
Author(s):  
Feng Qi ◽  
Can Kızılateş ◽  
Wei-Shih Du
Keyword(s):  
Chebyshev Polynomials ◽  
Closed Formula ◽  
Fibonacci Polynomials ◽  
Lucas Polynomials

In this paper, the authors present a closed formula for the Horadam polynomials in terms of a tridiagonal determinant and, as applications of the newly-established closed formula for the Horadam polynomials, derive closed formulas for the generalized Fibonacci polynomials, the Lucas polynomials, the Pell–Lucas polynomials, and the Chebyshev polynomials of the first kind in terms of tridiagonal determinants.

An efficient method to solve fuzzy Volterra integral equations using Fibonacci polynomials

2021 ◽  
pp. 1-16
Author(s):  
M. Darabi ◽  
T. Allahviranloo
Keyword(s):  
Exact Solution ◽  
Computational Complexity ◽  
Integral Equations ◽  
Collocation Method ◽  
Volterra Integral Equations ◽  
Fibonacci Polynomials ◽  
New Approach ◽  
Solution Convergence ◽  
Uniqueness Of The Solution ◽  
Recent Method

According to a huge interest in implementation of the fuzzy Volterra integral equations, especially the second kind, researchers have been investigating to solve such equations using numerical methods since analytical ones might not be accessible usually. In this research paper, we introduce a new approach based on Fibonacci polynomials collocation method to numerically solve them. Several properties of such polynomials were considered to implement in the collocation method due to approximate the solution of the second kind of fuzzy Volterra integral equations. We approved the existence, uniqueness of the solution, convergence and the error analysis of the proposed method in detail. In order to show the authenticity and applicability of the proposed method, we employed several illustrative examples. The numerical results show that the convergence and precision of the recent method were in a good settlement with the exact solution. Also, the calculations of the suggested method are simple and low computational complexity in respect to other methods as an advantage feature of the presented approach.

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