Some formulae for bivariate Fibonacci and Lucas polynomials [PDF]
arXiv, 2004 We derive a collection of identities for bivariate Fibonacci and Lucas polynomials using essentially a matrix approach as well as properties of such polynomials when the variables $x$ and $y$ are replaced by polynomials. A wealth of combinatorial identities can be obtained for selected values of the variables.
arxiv
The bi-periodic Horadam sequence and some perturbed tridiagonal 2-Toeplitz matrices: A unified approach. [PDF]
Heliyon, 2022 Anđelić M, da Fonseca CM, Yılmaz F.
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On some properties on bivariate Fibonacci and Lucas polynomials [PDF]
arXiv, 2007 In this paper we generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers satisfying remarkable recurrence relations.
arxiv
Extended Wang sum and associated products. [PDF]
PLoS One, 2022 Reynolds R, Stauffer A.
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Applications of the nonlinear Klein/Sinh-Gordon equations in modern physics: a numerical study
Mathematical Modelling and ControlIn this article, a hybrid numerical scheme based on Lucas and Fibonacci polynomials in combination with Störmer's method for the solution of Klein/Sinh-Gordon equations is proposed.
Ihteram Ali, Imtiaz Ahmad
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Representing derivatives of Chebyshev polynomials by Chebyshev polynomials and related questions
Open Mathematics, 2017 A recursion formula for derivatives of Chebyshev polynomials is replaced by an explicit formula. Similar formulae are derived for scaled Fibonacci numbers.
Prodinger Helmut
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Right Circulant Matrices with Generalized Fibonacci and\ Lucas Polynomials and Coding Theory [PDF]
arXiv, 2017 In this paper, we give two new coding algorithms by means of right circulant matrices with elements generalized Fibonacci and Lucas polynomials. For this purpose, we study basic properties of right circulant matrices using generalized Fibonacci polynomials $F_{p,q,n}\left( x\right) $, generalized Lucas polynomials $L_{p,q,n}\left( x\right) $ and ...
arxiv
VECTOR APPROACH TO A NEW GENERALIZATION OF FIBONACCI POLYNOMIAL
Journal of New Theory, 2017 Abstaract−In this paper we introduce a new generalization of Fibonacci polynomial and vectors of length d are defined for these Polynomials.
Ashok Dnyandeo Godase +1 more
doaj
Computational analysis of time-fractional models in energy infrastructure applications
Alexandria Engineering Journal, 2023 In this paper, we propose an effective numerical method to solve the one- and two-dimensional time-fractional convection-diffusion equations based on the Caputo derivative.
Imtiaz Ahmad +5 more
doaj
Vieta–Fibonacci-like polynomials and some identities [PDF]
, 2021 Wanna Sriprad +2 more
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