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设k∈N,f(z)为复平面上的超越亚纯函数,φ(z)、ak-1(z),…,a0(z)为f(z)的小函数,且φ(z)≠0.置P(f)(z)=f^(k)(z)+ak-1(z),f^(k-1)(z)+…+a1(z)f(z)+a0,(z),且P(f)(z)不恒为常数.当k≤4时,满足Nr)(r,1/f)=S(r,f);k≥5,满足N4)(r,1/f)=S(r,f),则T(r,f)〈20N^-(r,1/φfP-1)+s(r,f).