涉及分担函数的亚纯函数族的正规定则

Normal Criteria for Families of Meromorphic Functions That Share a Holomorphic Function

本文得到一个涉及分担函数的亚纯函数族的正规定则:设F是区域D内的一族亚纯函数,k,l是正整数,ψ(z)■0为区域D内全纯函数,且其零点重数至多为l,如果对F中的任意函数f,f(z)≠0,且f的所有极点重数都至少是l+1,如果F中的任意函数f与g满足f(k)与g(k)在D内分担ψ(z),那么F在D内正规.

This paper obtains a normal criterion of families of meromorphic functions, stating that a family F of mero morphic functions, whose multiplicities of all the poles are at least l ＋ 1, is normal in D, if for each f ∑ F, f（z） ≠ 0, and for each f∑ g∑ F, .f^（k） and g^（k） shareψ（z） in D, where ψ（z） ≠0 is a holomorphie function, whose multiplici- ties of zeros in D are at most l, where k, l are positive integers.