亚纯函数族与分担值相关的正规定则

研究了与分担值相关的亚纯函数正规族,设F是在区域D上的亚纯函数族,a是一个非零有限复数,对每一f∈F,f的极点重数至少为k,且满足Ef′(a)=Ef(a)和当f(z)=a时,有f(k)(z)=f(k+1)(z)=a,其中Ef(a)={z∈D:f(z)=a},则F在D上正规。

Sharing Values and Normality Criteria

Let F be a family of meromorphic in a domain D,and let a be a nonzero finite complex number,it is proved that F is a normal family,provided that for each f∈F,all poles of f are of multiplicity at least k,and Ef′（a）=Ef（a） and f（k）（z）=f（k＋1）（z）=a whenever f=a,where we write Ef（a）={z∈D：f（z）=a}.