导函数具有最大亏量和的亚纯函数

Meromorphic Functions with Derivative of Maximal Defect

设 f(z)是一下级μ有穷的亚纯函数。如对一正整数k则这里是的非零有穷亏值数,f^((0))=f 当 j 为负整数时,f^((f))是 f 的|j|次原函数(若存在)。

Let f(z) be a meromorphic function of lower order μ<∞.If for a positive integer k, sum from α to δ (α,f^((k)))=2,α∈. Then sum from f=-∞ to ∞ P_j≤μ Where P_j(j=0,±1,±2,…) are the numbers of non-zero finite defieient values of f^((j)).f^((o))=f and when j is negative,f^((j)) is defined as the |j|-th priraitive function of f(z) (if it exists).