Results 211 to 220 of about 454,219 (256)

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 ...
B. G. S. Doman, J. K. Williams
openaire   +3 more sources

On the period and the order of appearance of the sequence of Fibonacci polynomials modulo m

Journal of Discrete Mathematical Sciences and Cryptography, 2022
For a positive integer m, it is well known that the Fibonacci sequence modulo m, {Fn (mod m)}, is periodic and Fr is a multiple of m for some . The smallest possible value of r is called the order of appearance of m, denoted by r(m), in the Fibonacci ...
Kodchaphon Wanidchang, N. Kanasri
semanticscholar   +1 more source

A characterization of the Chebyshev and Fibonacci polynomials

Rendiconti del Circolo Matematico di Palermo, 1998
Usual orthogonal polynomials \(\{P_n(x)\}\) \((n=0,1,2,\ldots)\) satisfy a hypergeometric type differential equation: \[ (\alpha x^2+\beta x+\gamma)P_n''+(\delta x+\varepsilon)P_n' -n[\delta+(n-1)\alpha]P_n=0. \tag{HGE} \] Theorem 1. If a sequence of polynomials \(\{P_n\}\) satisfy (HGE) and the 3-term recurrence relation: \[ P_n(x)=xP_{n-1}(x)-P_{n-2}(
Paolo Ricci, Mauro Cuccoli
openaire   +3 more sources

Fibonacci polynomials for the numerical solution of variable‐order space‐time fractional Burgers‐Huxley equation

Mathematical methods in the applied sciences, 2021
In this article, the variable‐order (VO) space‐time fractional version of the Burgers‐Huxley equation is introduced with fractional differential operator of the Caputo type.
M. Heydari, Z. Avazzadeh
semanticscholar   +1 more source

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

Communications in Algebra, 2020
We define the Gauss Fibonacci polynomials. Then we give a formula for the Gauss Fibonacci polynomials by using the Fibonacci polynomials. The Gauss Lucas polynomials are described and the relation with Lucas polynomials are explained.
E. Özkan, Merve Taştan
semanticscholar   +1 more source

Shifted Vieta‐Fibonacci polynomials for the fractal‐fractional fifth‐order KdV equation

Mathematical methods in the applied sciences, 2021
In this article, the fractal‐fractional (FF) version of the fifth‐order KdV equation is introduced. The shifted Vieta‐Fibonacci (VF) polynomials are generated and adopted to establish a simple and accurate numerical method for solving this equation.
M. Heydari, Z. Avazzadeh, A. Atangana
semanticscholar   +1 more source

Numerical solution of fractal‐fractional differential equations system via Vieta‐Fibonacci polynomials fractal‐fractional integral operators

International journal of numerical modelling
The main idea of this work is to present a numerical method based on Vieta‐Fibonacci polynomials (VFPs) for finding approximate solutions of fractal‐fractional (FF) pantograph differential equations and a system of differential equations.
P. Rahimkhani, Y. Ordokhani, Sedigheh Sabermahani   +2 more
semanticscholar   +1 more source

On Generalizations of Dickson k-Fibonacci Polynomials

WSEAS Transactions on Mathematics
In this study, we define a Dickson k-Fibonacci polynomial inspired by Dickson polynomials and give some terms of these polynomials. Then we present the relations between the terms of Dickson k-Fibonacci polynomials.
Engin Ozkan, Hakan Akkuş
semanticscholar   +1 more source

On hyper (r, q)-Fibonacci polynomials

Mathematica Slovaca
Related to generalized arithmetic triangle, we introduce the hyper (r, q)-Fibonacci polynomials as the sum of these elements along a finite ray starting from a specific point, which generalize the hyper-Fibonacci polynomials. We give generating function,
H. Belbachir, Fariza Krim
semanticscholar   +1 more source

Complete homogeneous symmetric functions of Gauss Fibonacci polynomials and bivariate Pell polynomials

, 2020
: In this paper, we introduce a symmetric function in order to derive a new generating functions of bivariate Pell Lucas polynomials. We define complete homogeneous symmetric functions and give generating functions for Gauss Fibonacci polynomials, Gauss ...
N. Saba, A. Boussayoud
semanticscholar   +1 more source