Results 1 to 10 of about 7,865 (225)
On Period of the Sequence of Fibonacci Polynomials Modulo [PDF]
Discrete Dynamics in Nature and Society, 2013 It is shown that the sequence obtained by reducing modulo coefficient and exponent of each Fibonacci polynomials term is periodic. Also if is prime, then sequences of Fibonacci polynomial are compared with Wall numbers of Fibonacci sequences according ...
İnci Gültekin, Yasemin Taşyurdu
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Elliptic Solutions of Dynamical Lucas Sequences [PDF]
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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On Chebyshev Polynomials, Fibonacci Polynomials, and Their Derivatives [PDF]
Journal of Applied Mathematics, 2014 We study the relationship of the Chebyshev polynomials, Fibonacci polynomials, and their rth derivatives. We get the formulas for the rth derivatives of Chebyshev polynomials being represented by Chebyshev polynomials and Fibonacci polynomials.
Yang Li
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Fibonacci numbers and orthogonal polynomials [PDF]
Arab Journal of Mathematical Sciences, 2008 We prove that the sequence $(1/F_{n+2})_{n\ge 0}$ of reciprocals of the Fibonacci numbers is a moment sequence of a certain discrete probability, and we identify the orthogonal polynomials as little $q$-Jacobi polynomials with $q=(1-\sqrt{5})/(1+\sqrt{5})
Berg, Christian
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On Fourier integral transforms for $q$-Fibonacci and $q$-Lucas polynomials [PDF]
, 2012 We study in detail two families of $q$-Fibonacci polynomials and $q$-Lucas polynomials, which are defined by non-conventional three-term recurrences.
Andrews G E +18 more
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Extended Fibonacci numbers and polynomials with probability applications [PDF]
International Journal of Mathematics and Mathematical Sciences, 2004 The extended Fibonacci sequence of numbers and polynomials is introduced and studied. The generating function, recurrence relations, an expansion in terms of multinomial coefficients, and several properties of the extended Fibonacci numbers and ...
Demetrios L. Antzoulakos
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Hermite polynomials and Fibonacci oscillators [PDF]
Journal of Mathematical Physics, 2019 We compute the (q1, q2)-deformed Hermite polynomials by replacing the quantum harmonic oscillator problem to Fibonacci oscillators. We do this by applying the (q1, q2)-extension of Jackson derivative. The deformed energy spectrum is also found in terms of these parameters. We conclude that the deformation is more effective in higher excited states.
André A. Marinho, F. A. Brito
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The sums of the reciprocals of Fibonacci polynomials and Lucas polynomials [PDF]
Journal of Inequalities and Applications, 2012 AbstractIn this article, we consider infinite sums derived from the reciprocals of the Fibonacci polynomials and Lucas polynomials, and infinite sums derived from the reciprocals of the square of the Fibonacci polynomials and Lucas polynomials. Then applying the floor function to these sums, we obtain several new equalities involving the Fibonacci ...
Zhengang Wu, Wenpeng Zhang
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Generalized Fibonacci polynomials and Fibonomial coefficients [PDF]
Annals of Combinatorics, 2013 The focus of this paper is the study of generalized Fibonacci polynomials and Fibonomial coefficients. The former are polynomials {n} in variables s and t given by {0} = 0, {1} = 1, and {n} = s{n-1}+t{n-2} for n ge 2. The latter are defined by {n choose k} = {n}!/({k}!{n-k}!) where {n}! = {1}{2}...{n}.
Tewodros Amdeberhan +3 more
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Sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials [PDF]
Journal of Inequalities and Applications, 2018 In this paper, we consider sums of finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials and derive Fourier series expansions of functions associated with them. From these Fourier series expansions, we can express those
Taekyun Kim +3 more
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