关于亚纯函数族的一个正规定则  

One Normal Criteria of the Family of Meromorphic Functions

作　　者：范新华[1] 庞学诚[1] 

机构地区：[1]华东师范大学数学系,上海200062

出　　处：《华东师范大学学报（自然科学版）》2000年第2期18-22,共5页Journal of East China Normal University(Natural Science)

摘　　要：该文证明了一个正规定则 :设M是区域D内的亚纯函数族 ,若族中每个函数f(z)的极点之级≥s,f(z)的每个零点之级≤m ,ai(z) (i=0 ,1 ,2……k - 1 )为D内k个全纯函数 ,g(z)取q个互相判别的非零有穷值bj(j=1 ,2 ,……q)的点之级分别≥nj≥ 2 (j=1 ,2……q) ,这里 g(z)=f(k) (z) +ak -1 (z)f(k -1 ) (z) +…… +a0 (z)f(z) ,并且(q- 1 )k+1(q- 1 )m +1q - 1 Σqj=11nj(1 +ks) <1 ,则M在D内正规。In this paper we prove one normal criteria: Let M be a family of meromorphic functions in a domain D, a 0(z)……a k-1(z) be k holomorphic functions in D. If  f ∈ M, the order of each zero of F is ≥m, the order of each pole of F is ≥s, and g(z)=f- (k)(z)+a k-1(z)f- (k- 1)(z)+……+a 0(z)f(z), the order of each zero of g(z)-b j(j=1,2……q; b i≠ b j, i≠j, b j∈c/{0}) is ≥n j(≥2) and m, n j(j=1, 2……) are positive int egers satisfying (q-1)k+1(q-1)m+1q-1(1+ks)Σqj=11n j<1, then M is normal in D.

关 键 词：全纯函数 亚纯函数 正规定则 

分 类 号：O174.52[理学—数学]