Results 31 to 40 of about 14,400 (197)

Cube Polynomial of Fibonacci and Lucas Cubes [PDF]

Acta Applicandae Mathematicae, 2011
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Klavžar, Sandi, Mollard, Michel
openaire   +2 more sources

Novel Classes on Generating Functions of the Products of (p,q)-Modified Pell Numbers with Several Bivariate Polynomials

Mathematics
In this paper, using the symmetrizing operator δe1e22−l, we derive new generating functions of the products of p,q-modified Pell numbers with various bivariate polynomials, including Mersenne and Mersenne Lucas polynomials, Fibonacci and Lucas ...
Ali Boussayoud, Salah Boulaaras, Ali Allahem   +2 more
doaj   +1 more source

On Fourier integral transforms for $q$-Fibonacci and $q$-Lucas polynomials

, 2012
We study in detail two families of $q$-Fibonacci polynomials and $q$-Lucas polynomials, which are defined by non-conventional three-term recurrences.
Andrews G E, Askey R, Atakishiyev N M, Bers L, Cigler J, Cigler J, Cigler J, Dahlquist G, Decio Levi, Dunlap R A, Ismail M E H, Lang W, Maroni P, Matveev V B, Natig Atakishiyev, Orlando Ragnisco, Pedro Franco, Schroeder M, Slater L J   +18 more
core   +1 more source

Complex Factorizations of the Lucas Sequences via Matrix Methods

Journal of Applied Mathematics, 2014
Firstly, we show a connection between the first Lucas sequence and the determinants of some tridiagonal matrices. Secondly, we derive the complex factorizations of the first Lucas sequence by computing those determinants with the help of Chebyshev ...
Honglin Wu
doaj   +1 more source

The Gauss-Lucas Theorem and Jensen Polynomials [PDF]

Transactions of the American Mathematical Society, 1983
A characterization is given of the sequences { γ k } k = 0 ∞ \{ {\gamma _k}\}_{k = 0}^\infty with the property that, for any complex polynomial f ( z ) =
Craven, Thomas, Csordas, George
openaire   +1 more source

Novel Expressions for Certain Generalized Leonardo Polynomials and Their Associated Numbers

Axioms
This article introduces new polynomials that extend the standard Leonardo numbers, generalizing Fibonacci and Lucas polynomials. A new power form representation is developed for these polynomials, which is crucial for deriving further formulas.
Waleed Mohamed Abd-Elhameed, Omar Mazen Alqubori, Abdulrahim A. Alluhaybi, Amr Kamel Amin   +3 more
doaj   +1 more source

Chebyshev polynomials and their some interesting applications

Advances in Difference Equations, 2017
The main purpose of this paper is by using the definitions and properties of Chebyshev polynomials to study the power sum problems involving Fibonacci polynomials and Lucas polynomials and to obtain some interesting divisible properties.
Chen Li, Zhang Wenpeng
doaj   +1 more source

Relationship between Vieta-Lucas polynomials and Lucas sequences

, 2022
Let $w_n=w_n(P,Q)$ be numerical sequences which satisfy the recursion relation \begin{equation*} w_{n+2}=Pw_{n+1}-Qw_n. \end{equation*} We consider two special cases $(w_0,w_1)=(0,1)$ and $(w_0,w_1)=(2,P)$ and we denote them by $U_n$ and $V_n$ respectively. Vieta-Lucas polynomial $V_n(X,1)$ is the polynomial of degree $n$.
openaire   +2 more sources

Research on the Spinors of Jacobsthal and Jacobsthal–Lucas Hybrid Number Polynomials

Mathematics
By drawing on the concepts of Jacobsthal polynomials, Jacobsthal–Lucas polynomials, and hybrid numbers, this paper constructs, for the first time, a novel class of mathematical objects with recursive properties—namely, the sequences of Jacobsthal and ...
Yong Deng, Yanni Yang
doaj   +1 more source

A generalization of Lucas' theorem to vector spaces

International Journal of Mathematics and Mathematical Sciences, 1993
The classical Lucas' theorem on critical points of complex-valued polynomials has been generalized (cf. [1]) to vector-valued polynomials defined on K-inner product spaces.
Neyamat Zaheer
doaj   +1 more source