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\begin{equation*}
  Z - P = \frac{1}{2 \pi i} \int_\Gamma \frac{f'(z)}{f(z)}\, dz 
    = \frac{1}{2 \pi i} \int_\Gamma \frac{d}{dz} \log{f(z)}\, dz 
    = \frac{1}{2 \pi i} \Delta_\Gamma\log{f(z)}.
\end{equation*}
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