Solving polynomials with ordinary differential equations

Armengol Gasull, Hector Giacomini

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In this work we consider a given root of a family of n-degree polynomials as a one-variable function that depends only on the independent term. Then we prove that this function satisfies several ordinary differential equations (ODE). More concretely, it satisfies several simple separated variables ODE, a first order generalized Abel ODE of degree n−1 and an (n−1)-th order linear ODE. Although some of our results are not new, our approach is simple and self-contained. For n=2,3 and 4 we recover, from these ODE, the classical formulas for solving these polynomials.
Idioma originalEnglish
Pàgines (de-a)0624-643
Nombre de pàgines20
RevistaExpositiones Mathematicae
Estat de la publicacióAcceptat en premsa - 2021


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