关于亚纯函数正规族的正规定则

The normality criteria of meromorphic functions concerning shared value

讨论了亚纯函数涉及微分多项式分担值的正规性问题,证明了一个正规定则,推广和改进了原有的结果.设k,q(≥2)为正整数,F为D内的一族亚纯函数,若对任意的函数f∈F,f的零点的重数至少为k+1.H(f,f′,…,f(k))为f的微分多项式且Γ/γ|H<k+1.若对任意一组函数f,g∈F,(f(k))q+H(f,f′,…,f(k))与(g(k))q+H(g,g′,…,g(k))在D内分担1,则F在D内正规.

The normal family of mreomorphic functions concerning differential polynomials was studied.By using the method of shared values,the related result was improved and generalized.Let F be a family of meromorphic functions in a domain D such that each f∈F has zeros of multiplicity at least k＋1,let k,q（≥2） be two positive integers,and H（f,f′,…,f（k）） be a differential polynomial of f and Γ/γ｜Hk＋1.If,each pair of functions f and g in F,（f（k））q＋H（f,f′,…,f（k）） and（g（k））q＋H（g,g′,…,g（k）） share 1 IM,then F is normal in D.