多项式系数的齐次微分方程解的级与零点 The Order and Zeros of the Solutions of the Differential Equation with Polynomial Coefficients

摘要

本文研究的是齐次线性微分方程f(k)+A_k-1f(X-1)+...+A₀f=0的解的性质，其中系数A_j 是多项式，A_s 起控制作用，在满足某些条件的情况下，我们得到了：该方程的若干个线性无关解的级与零点收敛指数跟A_s 有紧密联系。 This paper investigates the properties of solutions to a linear differential equation f(k)+A_k-1f(X-1)+...+A₀f=0 , whose coefficients A_j are polynomial. If A_s plays a main role and satisfy some particular conditions, we draw a conclusion that A_s make a compact connection with the solutions of this equation.