On the relation between FDTD and Fibonacci polynomials
نویسنده
چکیده
Article history: Received 24 May 2010 Received in revised form 12 September 2010 Accepted 4 November 2010 Available online 27 November 2010
منابع مشابه
Dynamics of the Zeros of Fibonacci Polynomials
The Fibonacci polynomials are defined by the recursion relation Fn+2{x) = xF„+l(x) + Fn(x), (1) with the initial values Fx(x) = 1 and F2(x) = x. When x = l, Fn(x) is equal to the /1 Fibonacci number, Fn. The Lucas polynomials, Ln(x) obey the same recursion relation, but have initial values Li(x) = x and L^x) = x +2. Explicit expressions for the zeros of the Fibonacci and Lucas polynomials have ...
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In this paper we generalize to bivariate Fibonacci and Lucas polynomials, properties obtained for Chebyshev polynomials. We prove that the coordinates of the bivariate polynomials over appropriate bases are families of integers satisfying remarkable recurrence relations.
متن کاملGeneralized Bivariate Fibonacci-Like Polynomials and Some Identities
In [3], H. Belbachir and F. Bencherif generalize to bivariate polynomials of Fibonacci and Lucas, properties obtained for Chebyshev polynomials. They prove that the coordinates of the bivariate polynomials over appropriate basis are families of integers satisfying remarkable recurrence relations. [7], Mario Catalani define generalized bivariate polynomials, from which specifying initial conditi...
متن کاملOn Factorization of the Fibonacci and Lucas Numbers Using Tridiagonal Determinants
The aim of this paper is to give new results about factorizations of the Fibonacci numbers Fn and the Lucas numbers Ln. These numbers are defined by the second order recurrence relation an+2 = an+1+an with the initial terms F0 = 0, F1 = 1 and L0 = 2, L1 = 1, respectively. Proofs of theorems are done with the help of connections between determinants of tridiagonal matrices and the Fibonacci and ...
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عنوان ژورنال:
- J. Comput. Physics
دوره 230 شماره
صفحات -
تاریخ انتشار 2011