A NOTE TO THE NEVANJUNNA'S FUNDAMENTAL THEOREM

In this paper, the author extends Nevanlinna's second fundamental theorem and establishes the following inequality:Let $[p(s,u) = {A_v}(s){u^v} + {A_1}(s){u^{v - 1}} + cdots + {A_0}(s)]$be an irreducible two-variable polynomial and $f(s)$ a transcendental entire function, then$$[(nu - 1)T(r,f) < N(r,frac{1}{{p(z,f(z))}}) + S(r,f)]$$with $$[S(r,f) = O(log (rT(r,f)))n.e]$$where an. "n.e" means that the estimation holds for all large r with possibly an exceptional of finite measure when f is of infinite order.