关于全纯函数的正规定则

Normal Families of Holomorphic Function

研究了涉及微分多项式与公共值的全纯函数族的正规性问题,设F为区域D内的全纯函数族,n(≥1)、m(≥1)为2个正整数,b为有限常数.如果对F中的任意2个函数f(z)和g(z)有fn(fm-1)f′与gn(gm-1)g′在D内都以b为公共值,则F在D内正规.

In this paper, we study the problem of normal families of holomorphic function concerning differential polynomials and share values and prove the following theorem ： Let F be a family of holomorphic function in D , n,m be two positive integers. If for each pair of functionfand g in F f^n（f^n-1）f′and g^n（g^m-1）g′share a finite value b in D , then F is normal in D.