Results 11 to 20 of about 466,283 (262)
On Generalized Fibonacci Polynomials: Horadam Polynomials
Earthline Journal of Mathematical Sciences, 2022 In this paper, we investigate the generalized Fibonacci (Horadam) polynomials and we deal with, in detail, two special cases which we call them $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomials. We present Binet's formulas, generating functions, Simson's formulas, and the summation formulas for these polynomial sequences.
Y. Soykan
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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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On quaternion-Gaussian Fibonacci polynomials
Miskolc Mathematical Notes, 2023 Summary: In this paper, we define Gaussian Fibonacci quaternion polynomials and Gaussian Lucas quaternion polynomials. We also investigate some properties of these quaternion polynomials.
Tülay Yaǧmur
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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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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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Some identities involving Chebyshev polynomials, Fibonacci polynomials and their derivatives [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we will derive the explicit formulae for Chebyshev polynomials of the third and fourth kind with odd and even indices using the combinatorial method. Similar results are also deduced for their rᵗʰ derivatives.
Jugal Kishore, Vipin Verma
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Turkish Journal of Mathematics and Computer Science, 2023 In this article, the Apostol Bernoulli-Fibonacci polynomials are defined and various properties of Apostol Bernoulli-Fibonacci polynomials are obtained. Furthermore, Apostol Euler-Fibonacci numbers and polynomials are found. In addition, harmonic-based F exponential generating functions are defined for Apostol Bernoulli-Fibonacci numbers and Apostol ...
Elif GÜLAL, Naim TUGLU
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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
Basem Aref Frasin +4 more
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Novel Results for Two Generalized Classes of Fibonacci and Lucas Polynomials and Their Uses in the Reduction of Some Radicals [PDF]
Mathematics, 2022 The goal of this study is to develop some new connection formulae between two generalized classes of Fibonacci and Lucas polynomials. Hypergeometric functions of the kind 2F1(z) are included in all connection coefficients for a specific z.
Waleed Mohamed Abd-Elhameed +2 more
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Some Properties of the (p,q)-Fibonacci and (p,q)-Lucas Polynomials [PDF]
Journal of Applied Mathematics, 2012 Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper we consider the Pascal matrix and define a new generalization of Fibonacci polynomials ...
GwangYeon Lee, Mustafa Asci
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