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\frac{({z - f(a) })^{n}}{n!}
\lim_{ \omega \to a} \frac{d^{n-1}}{d\omega ^{n-1}} \left(\frac{\omega - a }{f(\omega) - f(a)}\right)^{n}
</math>
<em>In fact, integration by parts doesn't work for:</em>
:<math>
n=0\rightarrow
\frac{1}{2\pi i}
\oint_{C} \frac{ \omega f'(\omega)}{ f(\omega) - f(a) } d\omega =
\frac{1}{2\pi i}
\oint_{f(C)} \frac{ f^{-1}(u)}{ u - f(a) } du=
f^{-1}(f(a))=a
</math>
<em>Fortunately, writing the integral as a residue in the last line fixes the problem.</em>
==Applications==
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