摘要
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.
出处
《安康学院学报》
2010年第5期94-96,99,共4页
Journal of Ankang University
关键词
全纯函数
分担值
正规族
微分多项式
Holomorphic function
Shared values
Normality
Differential polynomial