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Fibonacci, Lucas, and Spread Polynomials
This note gives an elementary exposition of a variant of the spread polynomials in terms of Fibonacci and Lucas polynomials.
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Binomial Sums with Pell and Lucas Polynomials
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2021Pell and Pell-Lucas polynomials are given recursively by \(P_n(x)=2xP_{n-1}(x)+P_{n-2}(x)\) and \(Q_n(x)=2xQ_{n-1}(x)+Q_{n-2}(x)\), respectively, with initial conditions \(P_0(x)=0, P_1(x)=1, Q_0(x)=2, Q_1(x)=2x\). They generalize the Fibonacci and Lucas numbers, which correspond to \(F_n=P_n(\frac 12)\) and \(L_n=Q_n(\frac 12)\), respectively.
Dongwei Guo
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An alternative approach to Cigler’s q-Lucas polynomials
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hacène Belbachir
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ON SUMS OF BIVARIATE FIBONACCI POLYNOMIALS AND BIVARIATE LUCAS POLYNOMIALS
South East Asian J. of Mathematics and Mathematical Sciences, 2022In this paper, we present the sum of s+1 consecutive member of Bivariate Fibonacci Polynomials and Bivariate Lucas Polynomials and related identities consisting even and odd terms. We present its two cross two matrix and find interesting properties such as nth power of the matrix.
Panwar, Yashwant K. +2 more
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The Irregularity Polynomials of Fibonacci and Lucas cubes
Bulletin of the Malaysian Mathematical Sciences Society, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ömer Eğecioğlu +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 ...
Doman, B. G. S., Williams, J. K.
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\(d\)-Fibonacci and \(d\)-Lucas polynomials
2021Summary: Riordan arrays give us an intuitive method of solving combinatorial problems. They also help to apprehend number patterns and to prove many theorems. In this paper, we consider the Pascal matrix, define a new generalization of Fibonacci and Lucas polynomials called \(d\)-Fibonacci and \(d\)-Lucas polynomials (respectively) and provide their ...
Sadaoui, Boualem, Krelifa, Ali
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Lucas polynomials and power sums
2013 Information Theory and Applications Workshop (ITA), 2013The three — term recurrence xn + yn = (x + y) · (xn−1 + yn−1) − xy · (xn−2 + yn−2) allows to express xn + yn as a polynomial in the two variables x + y and xy. This polynomial is the bivariate Lucas polynomial. This identity is not as well known as it should be.
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