Nevanlinna ramification index (${\theta }_f(a)=\mathrm{liminf}[N(r;a)-\overline{N}(r;a)]/T_f(r)$)

The Nevanlinna ramification index is the normalized lower limiting integrated excess multiplicity over a target value, with pole orders used for infinity. It is an asymptotic value-distribution quantity, distinct from the integer ramification index of a holomorphic map at one source point. It can be positive even when the target has positive Nevanlinna deficiency.