亚纯函数的正规族与重值

Normal Families of Meromorphic Functions and Multiple Values

设F是区域D上的一族亚纯函数,ψ(■0)是区域D上的全纯函数,k为正整数,且对于任意的函数f∈F,都满足条件:f不取零,f(k)+∑k-1于等于(k+2)/k,且中括号内的微分多项式与ψ(z)无公共零点;其中ai(z)与bi(z)是区域D上全纯函数(i=0,1,…,k-1),则F在D内正规.

Let F be a family of meromorphic functions defined in a domain D,ψ(■0) be a holomorphic function in D,k is a positive integer.If f∈F,we have f≠0,f(k) +∑k-1 i=0aif(i) does not go to zero,all zeros of [f(k) +∑k-1 i=0bif(i)]-Ψ(z) have multiplicities at least(k+2)/k,and the differential polynomial [f(k) +∑k-1 i=0bif(i)] and the function ψ(z) have no common zeros,where ai(z) and bi(z) are holomorphic functions in D(i=0,1,…,k-1),then F is normal in D.