Results 21 to 30 of about 724,539 (169)
Melham's sums for some Lucas polynomial sequences [PDF]
Notes on Number Theory and Discrete MathematicsA Lucas polynomial sequence is a pair of generalized polynomial sequences that satisfy the Lucas recurrence relation. Special cases include Fibonacci polynomials, Lucas polynomials, and Balancing polynomials.
Chan-Liang Chung, Chunmei Zhong
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Symmetric and generating functions of generalized (p,q)-numbers
Kuwait Journal of Science, 2021 In this paper, we first define new generalization for (p,q)-numbers. Considering these sequence, we give Binet's formulas and generating functions of (p,q)-Fibonacci numbers, (p,q)-Lucas numbers, (p,q)-Pell numbers, (p,q)-Pell Lucas numbers, (p,q ...
Nabiha Saba +2 more
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Some remarks regarding the $(p,q)-$Fibonacci and Lucas octonion polynomials
Universal Journal of Mathematics and Applications, 2018 We investigate the $(p,q)-$Fibonacci and Lucas octonion polynomials. The main purpose of this paper is using of some properties of the $(p,q)-$ Fibonacci and Lucas polynomials. Also for present some results involving these octonion polynomials, we obtain
Arzu Özkoç Öztürk, Ayhan Porsuk
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Polynomial representations of the Lucas logarithm
Finite Fields and Their Applications, 2006 The authors provide results that are of interest for cryptosystems depending on the discrete logarithm problem. They look at the intractability of the so-called Lucas problem, which turns out to be computationally equivalent to the discrete logarithm problem over finite fields \(\mathbb F_{p^2}\). Moreover, they provide precise formulas for polynomials
Hassan Aly, Arne Winterhof
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Hyper-Fibonacci and Hyper-Lucas Polynomials [PDF]
, 2023 In this paper, hyper-Fibonacci and hyper-Lucas polynomials are defined and some of their algebraic and combinatorial properties such as the recurrence relations, summation formulas, and generating functions are presented.
Mersin, Efruz Özlem
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BıGaussian Pell and Pell-Lucas polynomials
Mathematica Montisnigri, 2022 In this paper, we define biGaussian Pell and Pell-Lucas Polynomials. We give Binet‘s formulas, generating functions, Catalan’s identities, Cassini’s identities for these polynomials. Matrix presentations of biGaussian Pell and Pell-Lucas polynomials are found. Also, NegabiGaussian Pell and Pell-Lucas Polynomials are defined.
Özkan, E., Alp, T.
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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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Multivariable Lucas Polynomials and Lucanomials
, 2019 17 ...
Allen, Edward E. +2 more
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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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