摘要:In this paper, the uniqueness of meromorphic functions is studied and the following result is proved:Let p(z) and q(z) be two coprime polynomials of degree n1 and n2 respectively, let f(z) and g(z) be two nonconstant transcendental meromorphic functions, and let n≥max{11,2n1+4n2+3} be a positive integer. If f n(z)f '(z) and gn(z)g'(z) share p(z)/q(z) CM, then f(z)=c1Q(z)eα(z), g(z)=c2Q-1(z)e-α(z), where c1,c2 are two constants, Q(z) is a rational function,and α(z) is a nonconstant polynomial satisfying(c1c2)n+1(Q'(z)/(Q(z)+α'(z))2≡-(p(z)/(q(z))2,or f(z)≡tg(z) for a constant t satisfying tn+1=1.%研究亚纯函数的惟一性,证明如下结果:设p(z)和q(z)分别为n1和n2次多项式且互素, f(z)和g(z)是两个超越亚纯函数,n≥max{11,2n1+4n2+3}是一个正整数,如果f n(z)f'(z),gn(z)g'(z)分担有理函数p(z)/q(z)CM,则f(z)=c1Q(z)eα(z),g(z)=c2Q-1(z)e-α(z),这里c1,c2是两个常数,Q(z)是一个有理函数,α(z)是一个非常数多项式,满足(c1c2)n+1(Q'(z)/(Q(z)+α'(z))2≡-(p(z)/q(z))2;或者f(z)≡tg(z),其中t是满足tn+1=1的常数.