Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequen...
Motivated by a problem proposed by Seiffert a quarter of century ago, we explicitly evaluate binomial sums with Pell and Lucas polynomials as weight functions. Their special cases result in several interesting identities concerning Fibonacci and Luca...
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...
Six well-known sequences (Fibonacci and Lucas numbers, Pell and Pell–Lucas polynomials, and Chebyshev polynomials) are characterized by quadratic linear recurrence relations. They are unified and reviewed under a common framework. Several usefu...
In this article, we present a study about the evolution of the COVID-19 pandemic in Turkey. The modelling of a new virus named SARS-CoV-2 is considered by an SIR model consisting of a nonlinear system of differential equations. A collocation approach...
This paper introduces two numerical algorithms for solving the fractional and classical Rosenau–Hyman equations. Certain shifted Pell–Lucas polynomials (SPLPs) are employed. New formulas for these polynomials are developed and used to ana...
In this paper, using the symmetrizing operator
This paper presents a Pell–Lucas collocation method for time-fractional partial integro-differential equations (TFPIDEs) with initial and boundary conditions, where the fractional derivative is taken in the Caputo sense. The unknown solution is...
The goal of this study is to develop some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. Hypergeometric functions of the kind
In this paper, we introduce a novel class of graphs referred to as the Horadam–Lucas cubes. This class extends the concept of Lucas cubes and retains numerous desirable properties associated with them. Horadam–Lucas cubes can also be view...
The Horadam sequence
In this study, we introduce generalized k-order Fibonacci and Lucas (F&L) polynomials that allow the derivation of well-known polynomial and integer sequences such as the sequences of k-order Pell polynomials, k-order Jacobsthal polynomials and k...