涉及分担值的两个亚纯函数族的正规定则

讨论2个亚纯函数族涉及分担值的正规性,证明如下结论:设F和G为区域D上的2个亚纯函数族,a1,a2,a3为3个互不相同的复数,k≥1,l≥0为整数.若亚纯函数族G正规,且对G的任意子列gn(z),有gn→g,且g■∞;若对任意的f∈F,零点重数大于等于k+1,且存在g∈G,使得f(k)(z)和g(l)(z)分担a1,a2,a3,则F在D上正规.

Normal Criteria about Two Families of Meromorphic Functions Involving Shared Values

We mainly discuss the normality of two families of meromorphic functions involving shared values,which was proved as follows：Let F andG be two families of functions meromor-phic on a domain D.Let a 1 ,a 2 ,a 3 be three distinct complex numbers,k ≥ 1,l ≥ 0 be two inte-gers.IfG is normal,and for any subsequence {g n （z）}ofG,g n → g,we have g ≠ ∞ on D.If for every f ∈ F,all zeros of f（z）are of multiplicity at least k ＋1 in D,there exists g ∈G such that f （k）（z）and g （l）（z）share the values a 1 ,a 2 ,a 3 ,then F is normal on D.