贵州师范大学学报:自然科学版
貴州師範大學學報:自然科學版
귀주사범대학학보:자연과학판
Journal of Guizhou Normal University(Natural Sciences)
2012年
4期
71-74
,共4页
亚纯函数%正规族%分担值
亞純函數%正規族%分擔值
아순함수%정규족%분담치
meromorphic functions%normal families%share value
设F为区域D上的一族亚纯函数,所有的零点重级至少是k,b为有穷非零复数,n,k为两正整数,P是有三个互相判别的零点的多项式.如果任意函数f,g∈F,P(f)(fn)(k)和P(g)(gn)(k)在D内分担b,则F在D内正规.
設F為區域D上的一族亞純函數,所有的零點重級至少是k,b為有窮非零複數,n,k為兩正整數,P是有三箇互相判彆的零點的多項式.如果任意函數f,g∈F,P(f)(fn)(k)和P(g)(gn)(k)在D內分擔b,則F在D內正規.
설F위구역D상적일족아순함수,소유적영점중급지소시k,b위유궁비령복수,n,k위량정정수,P시유삼개호상판별적영점적다항식.여과임의함수f,g∈F,P(f)(fn)(k)화P(g)(gn)(k)재D내분담b,칙F재D내정규.
Let F be a family of meromorphic functions in a domain D , all of whose zeros having multi-plicities at least k , let b be a finite nonzero complex number, n , k be two positive integers, and let P be a polynomial with three distinct zeros. If each pair of functionsf and g in F , P(f)(f^n)^(k), and p(g) ( g^n )^(k) share b in D , then F is normal on D.