与微分多项式相关的亚纯函数的正规族

Normal Families Of Meromorphic Functions Concerning Differentional Polynomials

设R为区域D上的一族亚纯函数,n,k(n≥k+1)均为正整数,b为一有限非零复数,a0(z),a1(z),...,ak-1(z)为D上的全纯函数,若对R中的任意函数f,f在D内的零点重数至少为n,f的极点重数至少为2,且L(f)=b f=b,其中L(f)(z)=f(k)(z)+k-∑1i=0ai(z)f(i)(z),则R在D内正规.

Suppose that R be a family of meromorphic functions in a domain D, n,k（n≥k＋1） be positive integers, and b be a finite complex number,a0（z）,a1（z）,…,k-1（z）are holomorphic functions. If A↓f∈ R, all zeros of fare of multiplicity at least n, the poles off are multiple and L∽=b=〉f=b, whereL∽（z）=f^（k）（z）＋k-1∑i=0ai（z）f^（i）（z）, then R is normal in D.