Results 11 to 20 of about 7,865 (225)
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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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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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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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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New expressions for certain polynomials combining Fibonacci and Lucas polynomials
AIMS MathematicsWe establish a new sequence of polynomials that combines the Fibonacci and Lucas polynomials. We will refer to these polynomials as merged Fibonacci-Lucas polynomials (MFLPs).
Waleed Mohamed Abd-Elhameed +1 more
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AxiomsTwo nonlinear Duffing equations are numerically treated in this article. The nonlinear fractional-order Duffing equations and the second-order nonlinear Duffing equations are handled.
Waleed Mohamed Abd-Elhameed +3 more
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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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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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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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