Results 11 to 20 of about 454,219 (256)
On Generalized Fibonacci Polynomials: Horadam Polynomials
Earthline Journal of Mathematical Sciences, 2022 In this paper, we investigate the generalized Fibonacci (Horadam) polynomials and we deal with, in detail, two special cases which we call them $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomials.
Y. Soykan
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A New Class of q-Fibonacci Polynomials [PDF]
The Electronic Journal of Combinatorics, 2003 We introduce a new $q$-analogue of the Fibonacci polynomials and derive some of its properties. Extra attention is paid to a special case which has some interesting connections with Euler's pentagonal number theorem.
Johann Cigler
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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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Indian Journal of Pure and Applied Mathematics, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Naim Tuglu, Semra Kuş, Can Kizilates
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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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On quaternion-Gaussian Fibonacci polynomials
Miskolc Mathematical Notes, 2023 In this paper, we define Gaussian Fibonacci quaternion polynomials and Gaussian Lucas quaternion polynomials. We also investigate some properties of these quaternion polynomials.
Tülay Yağmur
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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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On Convolved Generalized Fibonacci and Lucas Polynomials [PDF]
Applied Mathematics and Computation, 2013 We define the convolved h(x)-Fibonacci polynomials as an extension of the classical convolved Fibonacci numbers. Then we give some combinatorial formulas involving the h(x)-Fibonacci and h(x)-Lucas polynomials.
Ramírez, José L.
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Fibonacci Polynomials and Determinant Identities [PDF]
Turkish Journal of Analysis and Number Theory, 2014 The Fibonacci polynomials and Lucas polynomials are famous for possessing wonderful and amazing properties and identities. In this paper, some determinant identities of Fibonacci polynomials are describe. Entries of determinants are satisfying the recurrence relations of Fibonacci polynomials and Lucas polynomials.
Omprakash Sikhwal, Yashwant Vyas
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