涉及微分多项式的亚纯函数正规定则

The Normality Criteria of Meromorphic Functions Concerning Differential Polynomial

研究关于微分多项式的亚纯函数的正规定则,利用了Pang-Zalcman引理,将危合文和张惠玲的一些结果进行推广,得到了关于微分多项式以及分担值的亚纯函数的正规定则的结果。设F是定义在区域D上的一个亚纯函数族,若对于任一的f∈F, f的零点重级≥k+1,并且满足f+a(L(f))^(n)≠b(z), n≥k+2,其中k,n均为正整数,a≠0为常数,b(z)≠0在区域D内解析,则F在区域D内正规。设F是定义在区域D内的一族亚纯函数,族中任一函数的零点重级≥k+1, a,b均为非零有穷复数。任一取f, g∈F,若f+a(L(f))^(n),g+a(L(g))^(n)分担b, n,k∈N*,并且n≥2,则F在区域D内正规。

In this paper,the regular rule for meromorphic functions of differential polynomials are studied.The Pang-Zalcman Lemma is used to generalize some of the results of Wei Hewen and Zhang Huiling,the results of the higher-order derivatives to differential polynomials and some differential polynomials and meromorphic functions with shared values are obtained.Let F be a normal of meromorphic functions n on domain D,if for each function f∈F,all of whose zeros multiplicity at least k+1,f+a(L(f))^(n)≠b(z),n≥k+2,k,n be two positive integers,a≠0 be a constant,let b(z) be analytic functions in D,where b(z)≠0,then F is normal in D.let F be a normal of meromorphic functions on domain D,all of whose zeros multiplicity at least k+1,a≠0,b≠0 be two finite complex numbers.If for each function f,g∈F,n n f+a(L(f))^(n) and g+a(L(g))^(n) share the value b,n,k∈N,n≥2,then F is normal in D.