涉及微分多项式的亚纯函数的增长性

Growth of Meromorphic Functions Relate to Differential Polynomial

本文讨论了具有亏值的超越亚纯函数的增长性，证明了如下定理：设有下级为有穷的超越亚纯函数ｆ（ｚ）具有一亏值（有穷或否），（ｚ）＝ｆｎＱ［ｆ］＋ Ｐ［ｆ］为ｆ（ｚ）的微分多项式，其中Ｑ［ｆ］（≠０）与Ｐ［ｆ］（≠０）的各项系数均为级不超过的亚纯函数，且 Ｐ［ｆ］的权 ．又△（θｊ）（ｊ＝ １；２；…；ｑ； θｑ+1＝θ1+2π）为条从原点出发的半直线；且对有：其中为不依赖于的非负常数，则必有ｆ｛ｚ｝的级ｍａｘ。

In this paper, we discus the growth of meromorphic functions with a deficient value, and prove that. Suppose that f(z) is a transcendental meromorphic function of lower order with a deficient value, let =fnP[f] + P(f), where, P[f] and Q[f] are differential polynomials of f(z), and all of the orders of the coefficients of Q[f] and P[f] are less than , furthermore, the weight of P(f) is at most n - 3. If there exist finite number of rays satisfy with a positive number , for any small positive number , then max1 where, is the order of f(z).