机构地区: 华南师范大学数学科学学院
出 处: 《数学学报(中文版)》 2012年第3期525-534,共10页
摘 要: 研究了一类高阶齐次线性微分方程解的零点收敛指数,并得到当方程的系数A_0为整函数,其泰勒展式为缺项级数,并且A_0起控制作用时,方程f^((k))+A_(k-2)f^((k-2))+…+A_1f′+A_0f=0的任意两个线性无关解f_1,f_2满足max{λ(f_1),λ(f_2)}=∞,其中λ(f)表示亚纯函数.f的零点收敛指数. We investigate the exponent of convergence of zeros of solutions for some higher order homogeneous linear differential equation.When A_0 is an entire function that its taylor expansion is a gap power series and A_0 is the dominant coefficient,we proved that any two linearly independent solutions f_1 and f_2 of equation satisfy max{A(f_1),λ(f_2)} =∞,whereλ(f) denotes the exponent of convergence of zeros of meromorphic function f.