亚纯函数及其导数分担小函数集的唯一性

The Uniqueness of Meromorphic Functions and Their Derivatives Weighted-Sharing the Sets of Small Functions

研究了亚纯函数及其k阶导数权分担小函数集的唯一性,得到了:设k,n为正整数,f,g为开平面上超越亚纯函数,以∞为IM公共值,E(S1,f)=E(S1,g)且E1(S2,f(k))=E1(S2,g(k)l(≥2)∈N如果2nδ2+k(an,fn)+(nk+4)Θ(∞,f)>n(k+1)+4则f≡tg(tn=1)或[f(k)n(akn)][(gkn)(akn)]=]bn-(akn])2,并且文中还讨论了当l=0,1时的情形.这些定理推广和改进了先前的一些结果.

The uniqueness of meromorphic functions and their derivatives weakly weighted-sharing the sets of small functions is investigated,and the following theorem is obtained.Let k,n be two positive integers,f,g be nonconstant meromorphic functions in the complex plane C,f,g share ∞ IM,E（S1,f）=E（S1,g） and E1（S2,f（k））=E1（S2,g（k）l（≥2）∈N.If 2nδ2＋k（an,fn）＋（nk＋4）Θ（∞,f）n（k＋1）＋4 f≡tg（tn=1）= [f（k）n（akn）][（gkn）（akn）]=]bn-（akn]）2.Some results about l = 0,1 in the above theorem are obtained in this paper.These theorems of this paper extend and improve the previous results.