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

作　　者：丁培雄 陈宗煊[1] 

机构地区：[1]华南师范大学数学科学学院,广州

出　　处：《理论数学》2011年第3期214-223,共10页Pure Mathematics

摘　　要：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.

关 键 词：齐次线性微分方程 级 线性无关 

分 类 号：O1[理学—数学]