涉及重级零点和分担值的亚纯函数的正规定则

设F是区域D内的一族亚纯函数,k,m,q均为正整数,P(w)=wq+aq-1(z)wq-1+…+a1(z)w,H(f,f′,…,f(k))为f的微分多项式且满足γH*0;a(z)≠0,b(z)≠0为区域D内的解析函数,任意的f∈F的零点重级至少为k+1且满足f(z)=a(z)当且仅当P(f(k)(z))+H(f,f′,…,f(k))=b(z),则F在D内正规.

Normality of Meromorphic Functions with Multiple Zeros and Shared Values

Let F be a family of meromorphic function on D,let m,q,k,be positive numbers,P(ω)=ω~q+a_(q-1) (z)ω~(q-1)+…+a_1(z)ω is a polynomial. Let H(f,f~′,…,f~((k))) be a differential polynomial as above stated which satisfies γ_H~* >0,a(z)≠0,b(z)≠0 be some analytic functions in D. If, for each f∈ F, the zeros of f have multiplicity at least k+1, and if f (z)=a(z),that P(f~((k))(z))+H((f,f',…,f~((k))) =b(z) Then F is normal in D.