亚纯函数及其导函数的渐近值

Asymptotic Value of Meromorphic Function and Its Derived Function

定理设f(z)是下级μ有穷的亚纯函数,P_4是f^(i)(z)的非零有穷亏值数,而f^(0)(z)=f(z);当i为负整数时,f^(i)(z)为f(z)的(i)次原函数(若存在的话).若对某一正整数k, ??和?? 则f^((i))(z)(i=0,±1,±2,…)的所有有穷非零亏值都分别为它们的渐近值.

Let f(z) be a meromorphic function of lower order μ<∞, P_i(i=0,±1,±2,…)e the numbers of non-zero finite deficient values of f^((i))(z),f^((o))(z)=f(z).When i be negative,f^((i))(z) be defined as the |i|-th primitive function of f(z) (if it.exists).If for a positive integer k,??δ(a,f^((k))) =2 and ?? P_i=μ then every non-zero finite deficient value of f^((i))(z) (i=0, 1, 2,…) is an asymptotic value of f^((i))(z)