【摘要】 研究了亚纯函数的正规性,推广了徐焱和庞学成的正规定则.得到:设φ(0)是GC上的一列全纯函数族,且k∈N.设F是G上的一列亚纯函数族,且零点的级数为2,极点的级数至少为k+2.对于任意的f∈F,都有f(k)(z)+a1(z)f(k-1)(z)+…+ak(z)f(z)≠φ(z),这里的a1(z),a2(z),…,ak(z)是G上的全纯函数,则F在G正规.更多还原

【Abstract】 A normality criteria for families of meromorphic functions that concern the exceptional functions of derivatives is obtained,which improve and generalize related result of Xu and Pang.Let φ(■0)be a function holomorphic in a domain GC,and k∈N.Let F be a family of meromorphic functions defined in G,all of whose poles are multiple and whose zeros all have multiplicity at least k+2.If,for every function f∈F,f(k)(z)+a1(z)f(k-1)(z)+…+ak(z)f(z)≠φ(z),and a1(z),a2(z),…,ak(z)be holomorphic functions in domain G,then it is proved that F is normal in G.更多还原