与分担值相关的正规性

研究亚纯函数与其高阶导数分担值问题,把刘晓俊的结果推广到高阶导数,得到如下正规定则:设F为定义在D上的一族亚纯函数,a,b,c为三个互不相等的有穷复数,如对于任意的f∈■,f(z)=aL(z)=a,f∈{b,c}L(f)∈{b,c},且f-a的零点重级至少是k,这里L(f)=f(k)(z)+a1(z)f(k-1)(z)+...+ak(z)f(z),ai(z)(i=i,2,...,k)在D内解析,那么■在D内正规.

A normal family of shared value

Rereach of the problem of meromorphic functions and its higher derivative shared values was conducted.Result of Liu Xiaojun was extended to higher derivative.Let F be a family of meromorphic functions on the plain domain D,a,b and c are three distinct complex numbers.If for every f∈■,f(z)=aL(z)=a,f∈{b,c}L(f)∈{b,c},and the zeros of f-a are of multiplicity at least k,L(f)=f(k)(z)+a1(z)f(k-1)(z)+...+ak(z)f(z),and ai(z)(i=i,2,…,k) is analytic in D,then ■ is normal on D.