Results 121 to 130 of about 228 (148)

Lucas-type associated polynomials

Mathematica Applicanda, 2023
Summary: In this paper, we define a new type of Lucas polynomials known as Lucas-type associated polynomials and investigate their fundamental properties and identities. An interesting formula for Lucas-type associated polynomials can be derived using Leibniz's rule for derivatives, defined by Rodrigue's Lucas-type formula.
Guettai, Ghania, Laissaoui, Diffalah, Rahmani, Mourad   +2 more
openaire   +1 more source

Infinite sums for Fibonacci polynomials and Lucas polynomials

The Ramanujan Journal, 2018
In the paper, the following two interesting theorems are proved. Theorem 1. Let \(\{a_n\}\) be a sequence of numbers and \(|q| 0\) then \[\sum_{n=1}^{\infty} \frac{na_n}{F^2_{2n}(t)} = (t^2 + 4)\sum_{m=1}^{\infty} mb_m\beta(t)^{4m}\] and \[\sum_{n=1}^{\infty} \frac{na_n}{L^2_{2n}(t)} = \sum_{m=1}^{\infty} mb_m(\beta(t)^{4m} - 4\beta(t)^{8m});\] if \(t
Bing He, Ruiming Zhang
openaire   +2 more sources

Powers of a Matrix and the Generalized Lucas Polynomials

Journal of Mathematical Physics, 1971
The functions Lnk(r)(Φ1,⋯,Φn) are defined by Xr=∑k=1nLnk(r)Xn−k, where X is an indeterminate n × n matrix and Φ1, ⋯, Φn are the invariants of X (basic symmetric functions in the eigenvalues of X). In this paper the generalized Lucas polynomial Ln1(r) is expressed explicitly as a determinant of order r − n + 1 or as a ratio of two determinants of order ...
openaire   +2 more sources

On generalized Fibonacci and Lucas polynomials

Chaos, Solitons & Fractals, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nalli, Ayse, Haukkanen, Pentti
openaire   +1 more source

On the expansion of Fibonacci and Lucas polynomials

2009
Summary: Recently, \textit{H. Belbachir} and \textit{F. Bencherif} [J. Integer Seq. 11, No. 2, Article ID 08.2.6, 10 p., electronic only (2008; Zbl 1211.11019)] have expanded Fibonacci and Lucas polynomials using bases of Fibonacci- and Lucas-like polynomials.
openaire   +1 more source

On h(x)-Lucas quaternion polynomials.

Ars Comb., 2015
In this paper, we introduce h(x)-Lucas quaternion polynomials that generalize k-Lucas quaternion numbers that generalize Lucas quaternion numbers. Also we derive the Binet formula and generating function of h(x)-Lucas quaternion polynomial sequence.
openaire   +1 more source

The \(h(x)\)-Lucas quaternion polynomials

2017
Summary: In this paper, we study \(h(x)\)-Lucas quaternion polynomials considering several properties involving these polynomials and we present the exponential generating functions and the Poisson generating functions of the \(h(x)\)-Lucas quaternion polynomials.
openaire   +3 more sources

Irreducibility of Lucas and Generalized Lucas Polynomials

The Fibonacci Quarterly, 1974
Gerald E. Bergum, Verner E. Hoggatt
openaire   +1 more source

Some Novel Formulas of Lucas Polynomials via Different Approaches

Symmetry, 2023
W M Abd-Elhameed, Anna Napoli, Abd-Elhameed Waleed Mohamed   +2 more
exaly  

Lucas Polynomials and Power Sums

2022
The three - term recurrence x(n) + y(n) = (x + y) . (x(n-1) + y(n-1)) - xy . (x(n-2) + y(n-2)) allows to express x(n) + y(n) as a polynomial in the two variables x + y and xy. This polynomial is the bivariate Lucas polynomial. This identity is not as well known as it should be.
openaire   +1 more source