涉及微分多项式的亚纯函数的正规性

Differential Polynomial and Normal Family

R为单位圆Δ上的亚纯函数族,a为非零有限复数,k为一正整数,若对任意f∈R,没有零点,L(f)=f(k)+ak-1fk-1+…+a1f′+a0f为f的微分多项式,且有f.L(f)≠a,则R在Δ区域上正规.

Let R be a family of meromorphic functions on the unit disc A. Let a be a finite non - zero complex number and k be a positive integer. If for every function f∈R, f has no zeros, and L（f） =f^（k） ＋ ak-1f^k-1＋…＋a1f ＋a0f be differential polynomial of f.f· L（f）≠a,then R is normal on Δ.