一个涉及导数的亚纯函数的正规定则

A normal criterion of meromorphic functions concerning derivatives

研究了亚纯函数的正规性,改进了文献[1-4]中涉及导数的亚纯函数的正规定则中的部分条件,得到文中定理5。即设F为单位圆盘△上的一族亚纯函数,a,b为任意两个非零有穷复数,k,l为正整数且k>l,若对于任意的f(z)∈F,f(z)的零点重级至少为k+1,极点重级至少为2且f(k)(z)=a圯f(l)(z)≥b,则F在△上正规。

This paper studies the normality of a family of meromorphic functions, and obtains the following result 5 which improves part of the conditions in the references [1-4] ,a normal criterion on families of meromorphic functions concerning derivatives. That is,let F be a class of meromorphic functions in the unit circle, a,b be nonzero finite plural, and k ,l be positive integers and k〉l, for every f（z） ∈ F, the multiplicity of f（z） zero point is at least k＋l, the multiplicity of pole point is at least 2, andf^（k）（z）=a→f（l）（z）≥6, then F is normal in the unit circle.