关于Hennekemper的一个基本不等式

ON A BASIC INEQUALITY OF HENNEKEMPER

用与Ｈｅｎｎｅｋｅｍｐｅｒ不同的方法研究了（ｆｋ＋１）（ｋ）的值分布，将Ｈｅｎｎｅｋｅｍｐｅｒ所得的基本不等式推广至小函数情形，得到了如下定理：设ｆ为超越亚纯函数，Ｆ＝（ｆｋ＋１）（ｋ），ｋ∈Ｎ，φ为非零的小函数，则Ｔ（ｒ，ｆ）≤１＋２ｋ＋１４ｋ２＋２ｋ－１Ｎｒ，１ｆ＋４ｋ＋２４ｋ２＋２ｋ－１Ｎｒ，１Ｆ－φ＋Ｓ（ｒ，ｆ）．

Using a different way from Hennekempers one, this paper researches on the distribution of values of (f k+1 ) (k) and gives the following theorem: Suppose that f(z) is a transcendental meromorphic function, F=(f k+1 ) (k) , k∈N, φ is a nonzero small function, then T(r,f)≤1+2k+14k 2+2k-1Nr,1f+4k+24k 2+2k-1r,1F-φ+S(r,f).