Results 171 to 180 of about 523 (200)

\(d\)-Fibonacci and \(d\)-Lucas polynomials

2021
Summary: Riordan arrays give us an intuitive method of solving combinatorial problems. They also help to apprehend number patterns and to prove many theorems. In this paper, we consider the Pascal matrix, define a new generalization of Fibonacci and Lucas polynomials called \(d\)-Fibonacci and \(d\)-Lucas polynomials (respectively) and provide their ...
Sadaoui, Boualem, Krelifa, Ali
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Lucas polynomials and power sums

2013 Information Theory and Applications Workshop (ITA), 2013
The three — term recurrence xn + yn = (x + y) · (xn−1 + yn−1) − xy · (xn−2 + yn−2) allows to express xn + yn 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.
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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
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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
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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 ...
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On generalized Fibonacci and Lucas polynomials

Chaos, Solitons & Fractals, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nalli, Ayse, Haukkanen, Pentti
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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.
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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.
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Irreducibility of Lucas and Generalized Lucas Polynomials

The Fibonacci Quarterly, 1974
Gerald E. Bergum, Verner E. Hoggatt
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Some Novel Formulas of Lucas Polynomials via Different Approaches

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