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Some remarks for analytic functions related to Fibonacci polynomials and their applications
Timur Düzenlı +2 more
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Fibonacci and Lucas polynomials
Mathematical Proceedings of the Cambridge Philosophical Society, 1981The Fibonacci and Lucas polynomials Fn(z) and Ln(z) are denned. These reduce to the familiar Fibonacci and Lucas numbers when z = 1. The polynomials are shown to satisfy a second order linear difference equation. Generating functions are derived, and also various simple identities, and relations with hypergeometric functions, Gegenbauer and Chebyshev ...
B. G. S. Doman, J. K. Williams
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Supersymmetric Fibonacci polynomials
Analysis and Mathematical Physics, 2021It has long been recognized that Fibonacci-type recurrence relations can be used to define a set of versatile polynomials $$\{ p_{n} (z)\}$$ that have Fibonacci numbers and Chebyshev polynomials as special cases. We show that a tridiagonal matrix, which can
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A characterization of the Chebyshev and Fibonacci polynomials
Rendiconti del Circolo Matematico di Palermo, 1998Usual orthogonal polynomials \(\{P_n(x)\}\) \((n=0,1,2,\ldots)\) satisfy a hypergeometric type differential equation: \[ (\alpha x^2+\beta x+\gamma)P_n''+(\delta x+\varepsilon)P_n' -n[\delta+(n-1)\alpha]P_n=0. \tag{HGE} \] Theorem 1. If a sequence of polynomials \(\{P_n\}\) satisfy (HGE) and the 3-term recurrence relation: \[ P_n(x)=xP_{n-1}(x)-P_{n-2}(
Paolo Ricci, Mauro Cuccoli
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The Irregularity Polynomials of Fibonacci and Lucas cubes
Bulletin of the Malaysian Mathematical Sciences Society, 2020Irregularity of a graph is an invariant measuring how much the graph differs from a regular graph. Albertson index is one measure of irregularity, defined as the sum of | deg(u) - deg(v) | over all edges uv of the graph. Motivated by a recent result on the irregularity of Fibonacci cubes, we consider irregularity polynomials and determine them for ...
Ömer Eğecioğlu +2 more
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Fibonacci Polynomials their Properties and Applications
Zeitschrift für Analysis und ihre Anwendungen, 1996The paper deals with polynomials characterized by coefficients determined by successive elements of the Fibonacci sequence. Basic properties and applications of the Fibonacci polynomials are demonstrated. The index of concentration of Fibonacci polynomials at k -th degree, locations of ...
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On the characteristic polynomials of Fibonacci chains [PDF]
Journal of Physics A: Mathematical and General, 1992 Special diatomic linear chains with elastic nearest-neighbour interaction and the two masses distributed according to the binary Fibonacci sequence are studied.
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Deformable Derivative of Fibonacci Polynomials
2021The Fibonacci sequence is the most spectacular subject in mathematics, and the Fibonacci polynomials are generalizations of Fibonacci numbers made by various authors. The main objective of this research paper is to construct the relation between deformable derivative and Fibonacci polynomials.
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