论文标题
用普通微分方程求解多项式
Solving polynomials with ordinary differential equations
论文作者
论文摘要
在这项工作中，我们将n度多项式家族的给定根视为仅取决于独立项的单变量函数。然后，我们证明此函数满足几个普通的微分方程（ODE）。更具体地说，它满足了几个简单的分离变量ode，一种n-1度的一阶广义亚伯ode和（n-1）-th阶线性ode。尽管我们的某些结果并不新鲜，但我们的方法是简单且独立的。对于n = 2、3和4，我们从这些颂歌中恢复了解决这些多项式的经典公式。
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.
