涉及分担集的亚纯函数的正规定则

Normality Criterion of Meromorphic Functions Concerning Shared Set

设F为区域D上的亚纯函数族,S为具有三个元素的有穷复数集合,k为大于2的正整数,a为任何有穷复数.若对f∈F,f-a的零点和极点重数均≥k,且E(S,f)=E(S,f^((k)),则F在D内正规.

Let F be a family of meromorphic functions in a domain D and S be a set consisting of three distinct elements. Let a be a finite complex number and k（〉 2） be a positive integer. If each f ∈ f satisfies that the zeros and poles of f - a are of multiplicity ≥k and E（S, f） = E（S, f（k））, then f is normal in D.