Results 11 to 20 of about 524,049 (276)
Fibonacci numbers and orthogonal polynomials [PDF]
Arab Journal of Mathematical Sciences, 2008 We prove that the sequence $(1/F_{n+2})_{n\ge 0}$ of reciprocals of the Fibonacci numbers is a moment sequence of a certain discrete probability, and we identify the orthogonal polynomials as little $q$-Jacobi polynomials with $q=(1-\sqrt{5})/(1+\sqrt{5})
Berg, Christian
core +8 more sources
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
openaire +4 more sources
Fibonacci-Like Polynomials Produced by m-ary Huffman Codes for Absolutely Ordered Sequences [PDF]
arXiv, 2004 Fibonacci-like polynomials produced by m-ary Huffman codes for absolutely ordered sequences have been described.
A. B. Vinokur
arxiv +3 more sources
On the Derivatives of Bivariate Fibonacci Polynomials [PDF]
arXiv, 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
arxiv +5 more sources
Lucas, Fibonacci, and Chebyshev polynomials from matrices [PDF]
arXiv, 2021 A simple matrix formulation of the Fibonacci, Lucas, Chebyshev, and Dixon polynomials polynomials is presented. It utilizes the powers and the symmetric tensor powers of a certain matrix.
Jerzy Kocik
arxiv +3 more sources
Hermite polynomials and Fibonacci oscillators [PDF]
Journal of Mathematical Physics, 2019 We compute the (q1, q2)-deformed Hermite polynomials by replacing the quantum harmonic oscillator problem to Fibonacci oscillators. We do this by applying the (q1, q2)-extension of Jackson derivative. The deformed energy spectrum is also found in terms of these parameters. We conclude that the deformation is more effective in higher excited states.
André A. Marinho, F. A. Brito
openalex +6 more sources
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
openaire +3 more sources
The sums of the reciprocals of Fibonacci polynomials and Lucas polynomials [PDF]
Journal of Inequalities and Applications, 2012 Abstract In this article, we consider infinite sums derived from the reciprocals of the Fibonacci polynomials and Lucas polynomials, and infinite sums derived from the reciprocals of the square of the Fibonacci polynomials and Lucas polynomials.
Zhengang Wu, Wenpeng Zhang
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On quaternion-Gaussian Fibonacci polynomials
Miskolc Mathematical Notes, 2023 In this paper, we define Gaussian Fibonacci quaternion polynomials and Gaussian Lucas quaternion polynomials. We also investigate some properties of these quaternion polynomials.
Tülay Yağmur
openaire +3 more sources
Chebyshev-Fibonacci polynomial relations using generating functions [PDF]
arXiv, 2021 The main object of the paper is to reveal connections between Chebyshev polynomials of the first and second kinds and Fibonacci polynomials introduced by Catalan. This is achieved by relating the respective (ordinary and exponential) generating functions to each other.
Robert Frontczak, Taras Goy
arxiv +3 more sources