Results 151 to 160 of about 320 (182)

Distance Fibonacci Polynomials by Graph Methods

Symmetry, 2021
In this paper we introduce and study a new generalization of Fibonacci polynomials which generalize Fibonacci, Jacobsthal and Narayana numbers, simultaneously. We give a graph interpretation of these polynomials and we obtain a binomial formula for them.
Dominik Strzałka, S Wolski, Andrzej Włoch   +2 more
exaly   +2 more sources

On convolved generalized Fibonacci and Lucas polynomials [PDF]

Applied Mathematics and Computation, 2014
We define the convolved h(x)-Fibonacci polynomials as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the h(x)-Fibonacci and h(x)-Lucas polynomials. Moreover we obtain the convolved h(x)-Fibonacci polynomials form a family of Hessenberg matrices.
JOSÉ L Ramirez
exaly   +3 more sources

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Generalized Humbert polynomials via generalized Fibonacci polynomials

Applied Mathematics and Computation, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Weiping Wang
exaly   +3 more sources

Distance Fibonacci Polynomials

Symmetry, 2020
In this paper, we introduce a new kind of generalized Fibonacci polynomials in the distance sense. We give a direct formula, a generating function and matrix generators for these polynomials.
Urszula Bednarz, Małgorzata Wołowiec-Musiał   +1 more
exaly   +2 more sources

Distance Fibonacci Polynomials—Part II

Symmetry, 2021
In this paper we use a graph interpretation of distance Fibonacci polynomials to get a new generalization of Lucas polynomials in the distance sense.
Urszula Bednarz, Małgorzata Wołowiec-Musiał   +1 more
exaly   +2 more sources

Explicit, determinantal, recursive formulas, and generating functions of generalized Humbert–Hermite polynomials via generalized Fibonacci polynomials

Mathematical Methods in the Applied Sciences, 2023
In this paper, using the Faà di Bruno formula and some properties of the Bell polynomials of the second kind, we obtain a new explicit formula for the generalized Humbert–Hermite polynomials.
Can KIZILATEŞ
exaly   +2 more sources

Identities involving generalized Fibonacci-type polynomials

Applied Mathematics and Computation, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shi-Mei Ma
exaly   +3 more sources

Triangular numbers and generalized fibonacci polynomial

Mathematica Slovaca, 2022
AbstractIn the present paper, we study triangular numbers. We focus on the linear homogeneous recurrence relation of degree 3 with constant coefficients for triangular numbers. Then we deal with the relationship between generalized Fibonacci polynomials and triangular numbers.
openaire   +2 more sources

Generalized Fibonacci sequences via orthogonal polynomials

Applied Mathematics and Computation, 2012
For any four real numbers \(a, b, c\) and \(d\), the generalized Fibonacci sequence \(\{ Q_n \}^{\infty}_{n=0}\) is defined recursively by \[ Q_0 = 0, \;Q_1 = 1, \] \[ Q_n = \left \{ \begin{matrix} aQ_{n-1} + cQ_{n-2}, & \text{ if \(n\) is even} \\ bQ_{n-1} + dQ_{n-2}, & \text{ if \(n\) is odd} \end{matrix} \right. (n \geq 2).
J Petronilho
exaly   +3 more sources

SOME GENERALIZED FIBONACCI AND HERMITE POLYNOMIALS

JP Journal of Algebra, Number Theory and Applications, 2018
Summary: This paper defines a generalized Fibonacci polynomial and then compares its properties with those of Hermite polynomials and associated numbers.
Shannon, A. G., Deveci, Ömür
openaire   +2 more sources