与高阶导数分担多项式的整函数

Entire Functions Sharing Polynomial With Their Higher Order Derivative

摘要: 证明了如果~f~是非常数整函数满足超级~\sigma_2(f)<\frac12~,~~k~是一正整数,~如果~f~和~f^(k)~分担多项式~p(z)~~CM,~其中~p(z)=a_mz^m+a_m-1z^m-1+\cdots+a_0~~(~a_m\neq 0,~a_m-1,~\ldots,~a_0~均为常数)~,~那么~f^(k)(z)-p(z)=c(f(z)-p(z))~,~其中~c~是非零常数.

Abstract: It is shown that if f be a nonconstant entire function such that the hyper order \sigma_2(f)<\frac12 ,~k being a positive integer,~and if f and f^(k) share polynomial p(z) CM,~where p(z)=a_mz^m+a_m-1z^m-1+\cdots+a_0 with a_m\neq 0,~a_m-1,~\ldots,~a_0 are all constants,~then f^(k)(z)-p(z)=c(f(z)-p(z)) where c is a nonzero constant.