Solving polynomials with ordinary differential equations
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Giacomini, Hector (Université de Tours. Institut Denis Poisson)

Date:	2021
Abstract:	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.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Polynomial equation ; Ordinary differential equation ; Abel equations ; Elliptic and hyperelliptic integrals
Published in:	Expositiones Mathematicae, Vol. 39, Issue 4 (December 2021) , p. 624-643, ISSN 0723-0869

DOI: 10.1016/j.exmath.2021.06.001

Postprint 18 p, 333.3 KB

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