Results 1 to 10 of about 7,195 (140)
Distance Fibonacci Polynomials [PDF]
Symmetry, 2020 In this paper, we introduce a new kind of generalized Fibonacci polynomials in the distance sense. We give a direct formula, a generating function and matrix generators for these polynomials. Moreover, we present a graph interpretation of these polynomials, their connections with Pascal’s triangle and we prove some identities for them.
Urszula Bednarz +1 more
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Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers [PDF]
Mathematics, 2018 The aim of this paper is to research the structural properties of the Fibonacci polynomials and Fibonacci numbers and obtain some identities. To achieve this purpose, we first introduce a new second-order nonlinear recursive sequence. Then, we obtain our main results by using this new sequence, the properties of the power series, and the combinatorial ...
Ma, Yuankui, Zhang, Wenpeng
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(2, k)-Distance Fibonacci Polynomials [PDF]
Symmetry, 2021 In this paper we introduce and study (2,k)-distance Fibonacci polynomials which are natural extensions of (2,k)-Fibonacci numbers. We give some properties of these polynomials—among others, a graph interpretation and matrix generators. Moreover, we present some connections of (2,k)-distance Fibonacci polynomials with Pascal’s triangle.
Dorota Bród, Andrzej Włoch
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Generalized Fibonacci Polynomials [PDF]
Turkish Journal of Analysis and Number Theory, 2016 In this study, we present generalized Fibonacci polynomials. We have used their Binet’s formula and generating function to derive the identities. The proofs of the main theorems are based on special functions, simple algebra and give several interesting properties involving them.
Yashwant K. Panwar, B. Singh, V.K. Gupta
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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.
Andre A. Marinho, Francisco A. Brito
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Generalized Fibonacci Polynomials and Fibonomial Coefficients [PDF]
Annals of Combinatorics, 2014 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}.
Amdeberhan, Tewodros +3 more
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Inversion Polynomials for Permutations Avoiding Consecutive Patterns [PDF]
, 2014 In 2012, Sagan and Savage introduced the notion of $st$-Wilf equivalence for a statistic $st$ and for sets of permutations that avoid particular permutation patterns which can be extended to generalized permutation patterns.
Cameron, Naiomi, Killpatrick, Kendra
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Irreducibility of generalized Fibonacci polynomials
, 2022 Two ...
Flórez, Rigoberto, Saunders, J. C.
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Bernoulli-Fibonacci Polynomials
, 2020 By using definition of Golden derivative, corresponding Golden exponential function and Fibonomial coefficients, we introduce generating functions for Bernoulli-Fibonacci polynomials and related numbers. Properties of these polynomials and numbers are studied in parallel with usual Bernoulli counterparts.
Pashaev, Oktay K., Ozvatan, Merve
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On the roots of Fibonacci polynomials
Filomat, 2022 In this paper, we investigate Fibonacci polynomials as complex hyperbolic functions. We examine the roots of these polynomials. Also, we give some exciting identities about images of the roots of Fibonacci polynomials under another member of the Fibonacci polynomials class.
Birol, Furkan, Koruoğlu, Özden
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