Results 61 to 70 of about 7,865 (225)

Identities for the generalized Fibonacci polynomial

, 2017
A second order polynomial sequence is of Fibonacci type (Lucas type) if its Binet formula is similar in structure to the Binet formula for the Fibonacci (Lucas) numbers. In this paper we generalize identities from Fibonacci numbers and Lucas numbers to Fibonacci type and Lucas type polynomials.
Flórez, R., McAnally, N., Mukherjee, A.
openaire   +3 more sources

Series and Rational Solutions of the Second Kind Painlevé Equations by Using the Quantum Pseudospectral Method

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
The Painlevé equations and their series and rational solutions are essential in applied, pure mathematics and theoretical physics. Recently, quantum algorithms have helped to implement numerical algorithms more easily by performing linear algebra in our working. This article uses a hybrid of quantum computing schemes and spectral methods for the second
Saeid Abbasbandy, Shikha Binwal
wiley   +1 more source

Some Properties of Generalized Apostol-Type Frobenius–Euler–Fibonacci Polynomials

Mathematics
In this paper, by using the Golden Calculus, we introduce the generalized Apostol-type Frobenius–Euler–Fibonacci polynomials and numbers; additionally, we obtain various fundamental identities and properties associated with these polynomials and numbers,
Maryam Salem Alatawi, Waseem Ahmad Khan, Can Kızılateş, Cheon Seoung Ryoo   +3 more
doaj   +1 more source

Efficient Recovery of Linear Predicted Coefficients Based on Adaptive Steepest Descent Algorithm in Signal Compression for End‐to‐End Communications

Journal of Electrical and Computer Engineering, Volume 2025, Issue 1, 2025.
The efficiency of recovery and signal decoding efficacy at the receiver in end‐to‐end communications using linearly predicted coefficients are susceptible to errors, especially for highly compressed signals. In this paper, we propose a method to efficiently recover linearly predicted coefficients for high signal compression for end‐to‐end ...
Abel Kamagara, Abbas Kagudde, Baris Atakan, Andrea Tani   +3 more
wiley   +1 more source

On the power sums problem of bi-periodic Fibonacci and Lucas polynomials

AIMS Mathematics
This paper mainly discussed the power sums of bi-periodic Fibonacci and Lucas polynomials. In addition, we generalized these results to obtain several congruences involving the divisible properties of bi-periodic Fibonacci and Lucas polynomials.
Tingting Du , Li Wang
doaj   +1 more source

Subordination Properties of Bi‐Univalent Functions Involving Horadam Polynomials

Journal of Function Spaces, Volume 2025, Issue 1, 2025.
In this research, we investigate a family of q‐extensions defined on an open unit disk, which is based on bi‐univalent functions associated with differential subordination. Next, we define certain classes of bi‐univalent functions using generalized Horadam polynomials.
Ebrahim Amini, Shrideh Al-Omari, Abdul Rauf Khan   +2 more
wiley   +1 more source

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

A New Generalization of Leonardo Sequences: Biperiodic Leonardo Sequence

Journal of Mathematics, Volume 2025, Issue 1, 2025.
In this study, we define a new type of number sequence called biperiodic Leonardo sequence by the recurrence relation Lena,b=aLen−1+Len−2+1 (for even n) and Lena,b=bLen−1+Len−2+1 (for odd n) with the initial conditions Le0a,b=Le1a,b=1. We obtained the characteristic function, generating function, and Binet’s formula for this sequence and propose a ...
Hasan Gökbaş, Mohammad W. Alomari
wiley   +1 more source

New convolved Fibonacci collocation procedure for the Fitzhugh–Nagumo non-linear equation

Nonlinear Engineering
This article is dedicated to propose a spectral solution for the non-linear Fitzhugh–Nagumo equation. The proposed solution is expressed as a double sum of basis functions that are chosen to be the convolved Fibonacci polynomials that generalize the well-
Abd-Elhameed Waleed Mohamed, Al-Harbi Mohamed Salem, Atta Ahmed Gamal   +2 more
doaj   +1 more source

Some new results for the generalized bivariate Fibonacci and Lucas polynomials [PDF]

Mathematica Moravica
In this paper, new identities are obtained by using the generalized bivariate Fibonacci and Lucas polynomials. Firstly, several binomial summations and the closed formulas for summation of powers are investigated for these polynomials.
Yılmaz Nazmıye
doaj   +1 more source