关于整函数的微分多项式

ON DIFFERENTIAL POLYNOMIALS OF ENTIVES Zhang Zhanliang

设ｆ为超越整函数。本文证明了，对于任意正整数ｎ，ｍ，ｆｎ（ｆ）ｍ取任意非零有穷复数无穷多次。另外，对于形如ｆｎＱ１［ｆ］＋Ｑ２［ｆ］（这里Ｑ１［ｆ］、Ｑ２［ｆ］为ｆ的微分多项式）的函数，改进了Ｗ．

Let f be a transcendental entire, in this paper, it is shown that f n(f) m assumes all finite values except possibly zero infinitely often for positive integers n.m. Also, Doeringer's results in are improved for a function of the form f nQ 1+Q 2, where Q 1、Q 2 are differential polynomials in f.