= Radial zero-counting function
{title2=$n_f(r)=\sum_{|a|<r}\operatorname{ord}_a f$}
For a nonzero <holomorphic function>, $n_f(r)$ counts its <zeros of a function> in the centred <open disc> of radius $r$, with <multiplicity of a zero>. Thus a double zero counts twice, even though it is a single point. On every smaller closed <disk> in the domain the count is finite. The strict inequality $|a|<r$ specifies the convention at a zero modulus; elsewhere it agrees with counting in the closed <disk>. In the <polynomial circle log-mean> example the count is zero, one and two on the three displayed intervals.
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