涉及微分多项式的亚纯函数的正规定则

Normal Criterion of Meromorphic Functions Concerning Differential Polynomial and Shared Values

研究了亚纯函数族的正规性,推广了涉及导数的亚纯函数族的正规定则,得到了涉及微分多项式的亚纯函数正规族的一个结果.即:设F为单位圆盘上的一族亚纯函数,a为任一非零有穷复数,k为一正整数.若对任意的f(z)∈F,f(z)的零点重级至少为k+1,极点重级至少为2,且L(f)(z)和f(z)IM分担a,则F在单位圆盘上正规.

The normality of families of meromorphic functions was studied, and a result tor normat iamilies oi meromorphic functions concerning differential polynomial was obtained, which was extended from a normal criterion on families of meromorphic functions concerning derivative. The novel theorm shows that ： Let F be a class of meromorphie functions in the unit circle,a be a nonzero finite plural, and k be a positive integer, if for everyf（z） E F, the multi- plicity of zero point is at least k ＋ 1, the multiplicity of pole point is at least 2, and a is the IM shared value of L（f） （z） andf（z） , then F is normal in the unit circle.