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ON COMBINATORIAL IDENTITIES OF LUCAS AND FIBONACCI NUMBERS CONNECTED TO TCHEBYSHEV POLYNOMIALS
C Goutham, R. Rangarajan
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Some results on circulant matrices involving Fibonacci polynomials
Fatih Yılmaz +2 more
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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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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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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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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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Bivariate fibonacci like p–polynomials
Applied Mathematics and Computation, 2011Abstract In this article, we study the bivariate Fibonacci and Lucas p –polynomials ( p ⩾ 0 is integer) from which, specifying x , y and p , bivariate Fibonacci and Lucas polynomials, bivariate Pell and Pell-Lucas polynomials, Jacobsthal and Jacobsthal–Lucas polynomials, Fibonacci and Lucas p –polynomials, Fibonacci and Lucas p –numbers, Pell
Kocer, E. Gokcen +2 more
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Infinite sums for Fibonacci polynomials and Lucas polynomials
The Ramanujan Journal, 2018In this paper we establish certain infinite sums involving many arithmetical functions and the Fibonacci polynomials or the Lucas polynomials. Several of the sums are given explicitly in Jacobi theta functions.
Bing He, Ruiming Zhang
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