一个涉及极点重数的亚纯函数正规定则

Normal criterion for meromorphic functions involving multiplicity of poles

设F是平面区域D上的亚纯函数族,且族中每个函数的极点至少为k+1级.如果对所有f∈F,z∈D,有f(k)+af3≠b,这里a≠0,b为两个有穷复数,则F为D上的正规族.

Let F be a family of functions meromorphic on the plane domain D, all of whose poles are of multiplicity at least k ＋ 1. Suppose f ^（k） ＋ af^3≠b for all fE F and zE D , where a≠0, b are two finite complex numbers. Then F is normal on D.