Results 61 to 70 of about 524,049 (276)
A Study on Fibonacci and Lucas Bihypernomials
Discussiones Mathematicae - General Algebra and Applications, 2022 The bihyperbolic numbers are extension of hyperbolic numbers to four dimensions. In this paper we introduce and study the Fibonacci and Lucas bihypernomials, i.e., polynomials, which are a generalization of the bihyperbolic Fibonacci numbers and the ...
Szynal-Liana Anetta, Włoch Iwona
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Distance Fibonacci Polynomials by Graph Methods
Symmetry, 2021 In this paper we introduce and study a new generalization of Fibonacci polynomials which generalize Fibonacci, Jacobsthal and Narayana numbers, simultaneously. We give a graph interpretation of these polynomials and we obtain a binomial formula for them.
D. Strzałka, S. Wolski, A. Włoch
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Pure and Applied Mathematics QuarterlyThe Fibonacci polynomials $\big\{F_n(x)\big\}_{n\ge 0}$ have been studied in multiple ways. In this paper we study them by means of the theory of Heaps of Viennot. In this setting our polynomials form a basis $\big\{P_n(x)\big\}_{n\ge 0}$ with $P_n(x)$ monic of degree $n$. This given, we are forced to set $P_n(x)=F_{n+1}(x)$.
Garsia, A., Ganzberger, G.
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Contemporary MathematicsIn this article, we introduce a novel spectral algorithm utilizing Fibonacci polynomials to numerically solve both linear and nonlinear integro-differential equations with fractional-order derivatives. Our approach employs a quadrature-collocation method,
Youssri Hassan Youssri, A. G. Atta
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On the duals of the Fibonacci and Catalan-Fibonacci polynomials and Motzkin paths [PDF]
arXiv, 2021 We use the inversion of coefficient arrays to define dual polynomials to the Fibonacci and Catalan-Fibonacci polynomials, and we explore the properties of these new polynomials sequences. Many of the arrays involved are Riordan arrays. Direct links to the counting of Motzkin paths by different statistics emerge.
arxiv
On Certain Properties of Parametric Kinds of Apostol-Type Frobenius–Euler–Fibonacci Polynomials
AxiomsThis paper presents an overview of cosine and sine Apostol-type Frobenius–Euler–Fibonacci polynomials, as well as several identities that are associated with these polynomials.
Hao Guan +3 more
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European Journal of Pure and Applied MathematicsMaking use of a generalized bivariate Fibonacci polynomials, we propose a family of normalized regular functions ψ(ζ) = ζ + d2ζ2 + d3ζ3 + · · · , which are bi-univalent in the disc {ζ ∈ C : |ζ| < 1} involving (p, q)-derivative operator. We find estimates
B. Frasin +4 more
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MathematicsThis paper presents a comprehensive survey of the generalization of hybrid numbers and hybrid polynomials, particularly in the fields of mathematics and physics.
Can Kızılateş +2 more
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Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials
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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Solving systems of linear Fredholm integro-differential equations with Fibonacci polynomials
Ain Shams Engineering Journal, 2014 In this paper, we introduce a method to solve systems of linear Fredholm integro-differential equations in terms of Fibonacci polynomials. First, we present some properties of these polynomials then a new approach implementing a collocation method in ...
Farshid Mirzaee, Seyede Fatemeh Hoseini
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