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

本文研究的是齐次线性微分方程f(k)+Ak-1f(X-1)+...+A0f=0的解的性质,其中系数Aj 是多项式,As 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As 有紧密联系。

This paper investigates the properties of solutions to a linear differential equation f(k)+Ak-1f(X-1)+...+A0f=0 , whose coefficients Aj are polynomial. If As plays a main role and satisfy some particular conditions, we draw a conclusion that As make a compact connection with the solutions of this equation.