分担值与正规族

Sharing Values and Normal Families

设F是平面区域D上的亚纯函数族,a,b是两个有穷非零复数.如果■ff∈F,f(z)=a■f^((k))(z)=a,ff^((k))(z)=b■f^((k+1))(z)=b,且f-a的零点重数至少为k(k≥3),那么函数族F在D内正规;当k=2时,在条件a≠4b的情况下,同样有函数族F在D内正规.

Let F be a family of meromorphic functions on domain D, a, b be two non zero distinct finite complex numbers. If Vf εF, f（z） = a= f^（k）（z） = a, f^（k）（z） = b =f^（k＋l）（z） = b, and all zero points of f - a are of multiplicity at least k （k≥ 3）, then F is normal on D; in the case of k = 2, if a≠4b, then F is also normal on D.