关于φ(z)f(z)f^(k)(z)的值分布

On the Value Distrbution of φ(z)f(z)f^(k)(z)

得到在｜z｜<+∞内的超越亚纯函数f(z)涉及慢增长函数φ(z)的微分单项式φ(z)f(z)f(z)(k)的定量不等式:T(r,f)≤N1(r,f)+3 Nk)(r,1f)+ Nr,1φff(k)-1+S(r,f)其中φ(z)为非零亚纯函数,满足T(r,φ)=S(r,f);S(r,f)表示o(T(r,f))(r+∞),至多除去[0,+∞)内一线性测度有穷的集合.

Suppose f(z) is a transcendental meromorphic function in |z|<+∞. The conclusion is made that the following inequality hold which is related to the differential monomial φ(z)ff(k) of function f(z). T(r, f)≤N1(r, f)+3k)(r, 1f)+(r, 1φff(k)-1)+S(r, f)where φ(z) is nonzero slowly increasing function meromorphic in |z|<+∞ satisfying T(r, φ)=S(r, f) and S(r, f)=o(T(r, f))(r+∞) at the most outside the finite set of r of a linear measure in