一族亚纯函数的正规定则

Criteria for normality of a family of meromorphic functions

讨论亚纯函数族的正规性,推广庞学诚,陈怀惠和徐焱等人的结果.证明正规定则:设(1)n,k,l,t是4个正整数,其中,n≥2,n-1>k+1l+1t;(2)F是复平面中区域D上的一族亚纯函数,a是复平面内任一非零复数,h(z)为区域D内的任一连续函数;(3)族F中每个函数的极点和零点重数至少分别为l和t,且f(k)(z)-afn(z)≠h(z),∨z∈D,f∈F,则函数族F在区域D内正规.

It discussed the normality of a family of meromorphic functions which generalized the results due to Pang Xuecheng, Chen Huaihui and Xu Yan. We proved the following normal criteria：let （1）n,k,l,t be four positive integers,n≥2,n-1〉（k＋1）/l＋1/t.（2）F be a family of meromorphic functions in domain D a≠0,h（z）be a continuous function in D. （3）f∈F,the zeros and poles of fhave multiplicity at least l and t, and f^（k）（z）-af^n（z）≠h（z）,then F is normal in D.