关于超越亚纯函数f^((k))(z)+a(f^((k+1)))~n的值分布

The Value Distribution of the Atranscendental Meromorphic Function f^((k))(z)+a(f^((k+1)))~n

运用Nevanlinna亚纯函数理论方法,研究了超越亚纯函数的值分布理论,获得了如下结论,设f(z)为复平面上的超越亚纯函数,a为非零有穷复数,n和k是任意的正整数,且n≥2,则超越亚纯函数f(k)(z)+a(f(k+1))n取每一个有穷复数无穷多次,并推广了相关定理。

By using Nevanlinna＇s theory on meromorphic function,and studing value distribution theory of transcendental meromorphic function, this paper obtained the following conclusion： Let f （z） be a tran- scendental meromorphic function in the complex plane, a be a nonzero finite complex constant number,n and k were positive integer, and and n≥2 then the atranscendental meromorphic function f^（k）（z）＋a（f^（f＋1））^n assumes every finite complex number in finitely often, improving the relative theorems.