全纯函数与其微分多项式分担函数的正规性

Normality concerning Differential Polynomial in Holomorphic Functions Involve Shared Functions

研究全纯函数与其微分多项式分担函数,得到了如下的正规定则:设F是区域D内的全纯函数族,k是一正整数,h1(z),h2(z)在区域D内的解析,满足|h1(z)|2+|h2(z)|2≠0。若f∈F,f的零点重级至少为k,且f(z)=0|f(k)(z)|≤M(常数M>0),(z)=αi(z)L(Z)=αi(z),i=1,2,其中L(z)=f∞(z)+α1(z)f(k-1)(z)+…+αk(z)f(z)为f的微分多项式,αi(z)(i=1,2,…,k,k≥1)在D内解析,那么F在D内正规。

Researching the problem of holomorphic functions and its differential polynomial shared functions obtain normality criteria of families of holomorphic functions：Let F be a family of holomorphic functions in the plain domainD,k is a positive integer,（h1） z and（h2）z are two holomorohic functions in the plain domain D,and｜h1（z）｜2＋｜h2（z）｜2≠0.If f∈F,the zeros of f（z） are of multiplicity at least k,and f（z）=0｜f（k）（z）｜≤M（constant M0）,f（z）=αi（z）L（Z）=αi（z）,i=1,2,here L（z）=f（k）（z） ＋α1（z）f（k-1）（z）＋…＋αk（z）f（z）,αi（z）（i=1,2,…,k,k≥1） be analytic in D,then F is normal in D.