本文研究一类整函数系数高阶齐次线性微分方程解的零点分布.利用Nevanlinna值分布理论,得到当系数A_(k-1)的增长性起主要支配作用时,方程f(k)+A_(k-1)f(k-1)+···+A_0f=0任意超越解的零点收敛指数为无穷,推广了Langley和Bank等人的结果.
In this paper,we investigate the distribution of the zeros of the solutions for certain higher order homogeneous linear differential equations f(k)+ A_(k-1)f(k-1)+ · · · + A_0 f = 0with entire coefficients.By using the Nevanlinna's value distribution theory,we obtain that the exponent of convergence of zeros of every transcendental solution is infinite when A_(k-1)is the dominant coefficient,which extends the results of Langley and Bank.