| 全纯函数与其微分多项式分担函数的正规性 |
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| 引用本文： | 刘克笑.全纯函数与其微分多项式分担函数的正规性[J].安康学院学报,2010,22(5):94-96,99. |
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| 作者姓名： | 刘克笑 |
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| 作者单位： | 怀化学院,预科部,湖南,怀化,418008 |
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| 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。
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| 关 键 词： | 全纯函数 分担值 正规族 微分多项式 |
Normality concerning Differential Polynomial in Holomorphic Functions Involve Shared Functions |
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| LIU Kexiao.Normality concerning Differential Polynomial in Holomorphic Functions Involve Shared Functions[J].Journal of Ankang Teachers College,2010,22(5):94-96,99. |
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| Authors: | LIU Kexiao |
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| Institution: | LIU Kexiao(Department of Prior Courses,Huaihua University,Huaihua 418008,Hunan,China) |
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| Abstract: | 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 M>0),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. |
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| Keywords: | Holomorphic function Shared values Normality Differential polynomial |
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