涉及分担值的亚纯函数的正规性

Normality of Meromorphic Functions with Shared Values

研究一类亚纯函数族在分担值条件下的正规性.设F是单位圆Δ上的亚纯函数族,a≠b,b≠0,c≠0是3个有穷复数,f∈F,f(z)零点的重数至少为k(k≥2),且满足:(1)f(z)=0f(k)(z)+a1(z)f(k-1)(z)+a2(z)f(k-2)(z)+…+ak(z)f(z)=a;(2)f(k)(z)+b1(z)f(k-1)(z)+b2(z)f(k-2)(z)+…+bk(z)f(z)=b■f=c,其中ai(z),bi(z)(i=1,2,…,k)为Δ上的全纯函数,则F在Δ上正规.

The normality of meromophic functions with shared values is dealt with and the following result is achieved. Let F be a family of meromorphic functions on the unit circle △, and a≠b, b≠0, c≠0 are finite complex numbers. For f∈ F, the zeros of f（z） are of mulitiplicity, at least, k（k≥2）. If （1）f（z）=0 f^（k）（z）＋a1（z）f^（k-1）（z）＋a2（z）f^（k-2）（z）＋…＋ak（z）f（z）=a;（2）f^（k）（z）＋b1（z）f（k-1）（z）＋b2（z）f（k-2）（z）＋…＋bk（z）f（z）=6 f=c, ai（z） ,bi（z）（i = 1,2, …,k） are holomorphie functions on the unit circle A, then F is normal on unit circle △.