 Nevanlinna deficiency (source code)

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= Nevanlinna deficiency
{c}
{title2=$\delta_f(a)=1-\limsup N(r;a)/T_f(r)$}

For a nonconstant <meromorphic function>, its deficiency at a point of the <Riemann sphere> is the displayed asymptotic proportion missing from the full <Nevanlinna integrated counting function>. The <Nevanlinna first main theorem> bounds $N(r;a)$ by $T_f(r)+O(1)$ and identifies deficiency with the lower limiting normalized proximity. An omitted value has deficiency one.

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