Resultants of Chebyshev Polynomials: A Short Proof

Louboutin, Stéphane

doi:10.4153/cmb-2012-002-1

Cited by 5 publications

(1 citation statement)

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“…The first formula for the resultant of two cyclotomic polynomials was given by Apostol [3]. Some other papers have been dedicated to the study of resultant of Chebyshev Polynomials [6,19,24,28]. In this paper we deduce simple closed formulas for the resultants of a big family of GFPs.…”

Section: Introductionmentioning

confidence: 99%

The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials

Flórez,

Higuita,

Ramírez

2018

Preprint

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A second order polynomial sequence is of Fibonacci-type (Lucas-type) if its Binet formula has a structure similar to that for Fibonacci (Lucas) numbers. Known examples of these type of sequences are: Fibonacci polynomials, Pell polynomials, Fermat polynomials, Chebyshev polynomials, Morgan-Voyce polynomials, Lucas polynomials, Pell-Lucas polynomials, Fermat-Lucas polynomials, Chebyshev polynomials.The resultant of two polynomials is the determinant of the Sylvester matrix and the discriminant of a polynomial p is the resultant of p and its derivative. We study the resultant, the discriminant, and the derivatives of Fibonacci-type polynomials and Lucastype polynomials as well combinations of those two types. As a corollary we give explicit formulas for the resultant, the discriminant, and the derivative for the known polynomials mentioned above.

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Section: Introductionmentioning

confidence: 99%