Results 21 to 30 of about 228 (148)
Elliptic Solutions of Dynamical Lucas Sequences
Entropy, 2021 We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system
Michael J. Schlosser, Meesue Yoo
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Polynomials of binomial type and Lucas’ Theorem [PDF]
Proceedings of the American Mathematical Society, 2015 We present various constructions of sequences of polynomials satisfying the Binomial Theorem in finite characteristic based on the theory of additive polynomials. Various actions on these constructions are also presented. It is an open question whether we have then accounted for all sequences in finite characteristic which satisfy the Binomial Theorem.
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Chords of an Ellipse, Lucas Polynomials, and Cubic Equations [PDF]
The American Mathematical Monthly, 2020 18 pages, 1 table, 2 figures. This is the "Accepted Manuscript" of the article, published in the American Mathematical Monthly on Sept. 21, 2020.
Ben Blum-Smith, Japheth Wood
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A Study on Fibonacci and Lucas Bihypernomials
Discussiones Mathematicae - General Algebra and Applications, 2022 The bihyperbolic numbers are extension of hyperbolic numbers to four dimensions. In this paper we introduce and study the Fibonacci and Lucas bihypernomials, i.e., polynomials, which are a generalization of the bihyperbolic Fibonacci numbers and the ...
Szynal-Liana Anetta, Włoch Iwona
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Multivariable Lucas Polynomials and Lucanomials
, 2019 17 ...
Allen, Edward E. +2 more
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Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials
Discrete Dynamics in Nature and Society, 2012 We define the incomplete bivariate Fibonacci and Lucas 𝑝-polynomials. In the case 𝑥=1, 𝑦=1, we obtain the incomplete Fibonacci and Lucas 𝑝-numbers. If 𝑥=2, 𝑦=1, we have the incomplete Pell and Pell-Lucas 𝑝-numbers.
Dursun Tasci +2 more
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p-Analogue of biperiodic Pell and Pell–Lucas polynomials [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this study, a binomial sum, unlike but analogous to the usual binomial sums, is expressed with a different definition and termed the p-integer sum. Based on this definition, p-analogue Pell and Pell–Lucas polynomials are established and the generating
Bahar Kuloğlu +2 more
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On the power sum problem of Lucas polynomials and its divisible property
Open Mathematics, 2018 The main purpose of this paper is to use the mathematical induction and the properties of Lucas polynomials to study the power sum problem of Lucas polynomials. In the end, we obtain an interesting divisible property.
Xiao Wang
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Numerical method for fractional Advection–Dispersion equation using shifted Vieta–Lucas polynomials
Results in Physics, 2023 In the pursuit of creating more precise and flexible mathematical models for complex physical phenomena, this study constructs a unique fractional model for the Advection–Dispersion equation.
Mohammad Partohaghighi +3 more
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MathematicsIn 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 +2 more
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