Results 11 to 20 of about 962 (220)
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
Yuankui Ma, Wenpeng Zhang
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Incomplete Bivariate Fibonacci and Lucas đť‘ť-Polynomials [PDF]
Discrete Dynamics in Nature and Society, 2012 We define the incomplete bivariate Fibonacci and Lucas 𝑝-polynomials. In the case 𝑥=1, 𝑦=1, we obtain the incomplete Fibonacci and Lucas 𝑝-numbers. If 𝑥=2, 𝑦=1, we have the incomplete Pell and Pell-Lucas 𝑝-numbers.
Dursun Tasci +2 more
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On Convolved Fibonacci Polynomials
MathematicsThis work delves deeply into convolved Fibonacci polynomials (CFPs) that are considered generalizations of the standard Fibonacci polynomials. We present new formulas for these polynomials. An expression for the repeated integrals of the CFPs in terms of
Waleed Mohamed Abd-Elhameed +2 more
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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 ...
Ä°nci GĂĽltekin, Yasemin TaĹźyurdu
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HOMFLY Polynomials of Torus Links as Generalized Fibonacci Polynomials [PDF]
The Electronic Journal of Combinatorics, 2015 The focus of this paper is to study the HOMFLY polynomial of $(2,n)$-torus link as a generalized Fibonacci polynomial. For this purpose, we first introduce a form of generalized Fibonacci and Lucas polynomials and provide their some fundamental properties.
Kemal Taşköprü, İsmet Altıntaş
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GENERALIZED IDENTITIES OF BIVARIATE FIBONACCI AND BIVARIATE LUCAS POLYNOMIALS
Journal of Amasya University the Institute of Sciences and Technology, 2020 In this paper, we present generalized identities of bivariate Fibonacci polynomials and bivariate Lucas polynomials and related identities consisting even and odd terms. Binet’s formula will employ to obtain the identities.
Jaya Bhandari +2 more
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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 BrĂłd, Andrzej WĹ‚och
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AIMS Mathematics, 2023 This paper aims to give generating functions for the new family of polynomials, which are called parametric types of the Apostol Bernoulli-Fibonacci, the Apostol Euler-Fibonacci, and the Apostol Genocchi-Fibonacci polynomials by using Golden calculus ...
Can Kızılateş , Halit Öztürk
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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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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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