Results 11 to 20 of about 302 (175)
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
Wenpeng Zhang
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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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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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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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Mathematics, 2018 This paper is concerned with representing sums of the finite products of Chebyshev polynomials of the second kind and of Fibonacci polynomials in terms of several classical orthogonal polynomials.
Taekyun Kim, Dae Kim, Jongkyum Kwon
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Some Properties of Generalized Apostol-Type Frobenius–Euler–Fibonacci Polynomials
MathematicsIn this paper, by using the Golden Calculus, we introduce the generalized Apostol-type Frobenius–Euler–Fibonacci polynomials and numbers; additionally, we obtain various fundamental identities and properties associated with these polynomials and numbers,
Maryam Salem Alatawi +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 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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On the derivatives of bivariate Fibonacci polynomials [PDF]
Notes on Number Theory and Discrete Mathematics, 2018 In this study, the new algebraic properties related to bivariate Fibonacci polynomials has been given. We present the partial derivatives of these polynomials in the form of convolution of bivariate Fibonacci polynomials. Also, we define a new recurrence relation for the r-th partial derivative sequence of bivariate Fibonacci polynomials.
KARADUMAN, Erdal, Cakmak, Tuba
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