涉及分担值的一个正规定则

A Normal Criterion Concerning Shared Values

设F是区域D内的一族亚纯函数,a,e是两个有穷复数,b,c,d是三个非零有穷复数,k≥2是一个正整数.若对于F中的任意函数f,f-e的零点重级至少为k,f(z)=af^((k))(z)=b,f^((k))(z)=c■f^((k+1))(z)=d,则F在D内正规.当k=1时,如果b≠(n+1)c,其中n为正整数,结论同样成立.

Let F be a family of meromorphic functions on a plane domain D,let a,e be two finite complex numbers,and 6,c,d be three nonzero finite complex numbers.If,for each f∈F,all the zeros of f-e are of multiplicity at least k≥2,f（z）=a-f^（（k））（z）=b,and f^（（k））（z）=c→ f^（（k＋1））（z）=d,then F is a normal family on D.The same result holds for k=1 so long as b≠（n＋1）c,n=1,2….