A note to the Nevanlinna's fundamental theorem (Q1824723)

The author extends Nevanlinna's second fundamental theorem and establishes the following inequality: Let \(p(s,u)=A_{\nu}(z)u^{\nu}+A_ 1(z)u^{\nu -1}+...+A_ 0(z)\) be an irreducible two-variable polynomial and f(z) a transcendental entire function, then \[ (\nu -1)T(r,f)<N(r,(p(z,f(z)))^{-1})+S(r,f) \] with \[ S(r,f)=O(\log (rT(r,f)))\quad n.e., \] where ``n.e.'' means that the estimation holds for all large r with possibly an exceptional set of finite measure when f is of infinite order.