Binomials transformation formulae for scaled Fibonacci numbers
Open Mathematics, 2017 The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined
Hetmaniok Edyta +2 more
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Melham's sums for some Lucas polynomial sequences [PDF]
Notes on Number Theory and Discrete MathematicsA Lucas polynomial sequence is a pair of generalized polynomial sequences that satisfy the Lucas recurrence relation. Special cases include Fibonacci polynomials, Lucas polynomials, and Balancing polynomials.
Chan-Liang Chung, Chunmei Zhong
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Properties of the Ammann–Beenker Tiling and its Square Periodic Approximants
Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.This review article is intended for those seeking to understand the geometrical properties of one well‐known two‐dimensional quasiperiodic tiling, namely the Ammann‐Beenker tiling. This eight‐fold symmetric tiling has been a preferred starting point for studies of electronic properties of quasicrystals, due to its relatively simple structure as ...
Anuradha Jagannathan, Michel Duneau
wiley +1 more source
ON THE ZEROS OF THE DERIVATIVES OF FIBONACCI AND LUCAS POLYNOMIALS
Journal of New Theory, 2015 The purpose of this article is to derive some functions which map the zeros of Fibonacci polynomials to the zeros of Lucas polynomials. Also we find some equations which are satisfied by F 0 n (x) and so L 00 n (x).
Nihal Yılmaz Özgür +1 more
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Coefficient Estimate and Fekete-Szeg\"{o} Problems for Certain New Subclasses of Bi-univalent Functions Defined by Generalized Bivariate Fibonacci Polynomial [PDF]
Sahand Communications in Mathematical AnalysisThis article deals with two new subclasses of analytic and bi-univalent functions in the open unit disk, which is defined by applying subordination principle between analytic functions and the generalized Bivariate Fibonacci polynomials.
Rumeysa Öztürk, İbrahim Aktaş
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Binomial Fibonacci sums from Chebyshev polynomials [PDF]
, 2023 Kunle Adegoke +2 more
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The binomial sums for four types of polynomials involving floor and ceiling functions
Electronic Research ArchiveSeveral binomial sums are established for the Pell polynomials and the Pell-Lucas polynomials, as well as two types of the Chebyshev polynomials and the Fibonacci-Lucas numbers, which include two special cases proposed by Hideyuki Othsuka in 2024.
Qingjie Chai, Hanyu Wei
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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.
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A fast Fibonacci wavelet-based numerical algorithm for the solution of HIV-infected CD4+T cells model. [PDF]
Eur Phys J Plus, 2023 Vivek, Kumar M, Mishra SN.
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On the finite reciprocal sums of Fibonacci and Lucas polynomials
AIMS Mathematics, 2019 In this note, we consider the finite reciprocal sums of Fibonacci and Lucas polynomials and derive some identities involving these sums.
Utkal Keshari Dutta, Prasanta Kumar Ray
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