Derivative Sequences of Fibonacci and Lucas Polynomials

Filipponi, Piero; Horadam, A. F.

doi:10.1007/978-94-011-3586-3_12

Cited by 74 publications

(35 citation statements)

References 3 publications

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“…Additional comment: With regard to Conjectures 1-7 in [1], some of which were known by us to be true, we wish to record that, in private correspondence with us, both Richard Andre-Jeannin and David Zeitlin have independently established the validity of these Conjectures.…”

Section: =0mentioning

confidence: 95%

Derivative Sequences of Fibonacci and Lucas Polynomials

Filipponi¹,

Horadam²

1991

Applications of Fibonacci Numbers

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Section: =0mentioning

confidence: 95%

Derivative Sequences of Fibonacci and Lucas Polynomials

Filipponi¹,

Horadam²

1991

Applications of Fibonacci Numbers

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“…where x is an indeterminate and F 1 (x) = 0 and F 2 (x) = 1.This polynomials can be expressed by means of the Binet form [3]…”

Section: Fibonacci Polynomialsmentioning

confidence: 99%

Solving linear integral equations with Fibonacci polynomial

Nadir¹

2018

Malaya J. Mat.

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The goal of this work is to seek an approximate solution of Fredholm and Volterra integral equations using Fibonacci polynomials with hat basis functions, in order to obtain a variational problem and reduce this one to a linear system, where its solution is to find the Fibonacci coefficients of the unknown function and thereafter the solution of the equation. The convergence of this method is assured and the high accuracy of the error estimation is compared with other numerical methods.

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“…is the estimated error function obtained with the help of the residual error function. Here a i,n and a * i,n are the unknown Lucas coefficients and L n (x) (n = 0, 1, 2, ..., N) are the Lucas polynomials defined by [28,29],…”

Section: Preliminariesmentioning

confidence: 99%

On the solution of differential equation system characterizing curve pair of constant breadth by the Lucas collocation approximation

Çetin¹,

Kocayiğit²,

Sezer³

2016

ntmsci

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In this study, for solving linear differential equation system characterizing curve pair of constant breadth according to Bishop frame in Euclidean 3-space, a new collocation method based on Lucas polynomials is introduced and hence the curve pair of constant breadth is determined. Furthermore, an error analysis based on residual error function is given for the method. To demonstrate the accuracy and effciency of the method, an example is given with the help of computer programmes Maple and Matlab.

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Derivative Sequences of Fibonacci and Lucas Polynomials

Cited by 74 publications

References 3 publications

Derivative Sequences of Fibonacci and Lucas Polynomials

Derivative Sequences of Fibonacci and Lucas Polynomials

Solving linear integral equations with Fibonacci polynomial

On the solution of differential equation system characterizing curve pair of constant breadth by the Lucas collocation approximation

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