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Adamnemecek (talk | contribs) added mention of inverse function theorem |
Important comment. |
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\frac{f'(\omega) d\omega}{(f(\omega) - f(a))^{n+1} }
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</math>
''In fact, integration by parts doesn't work for:''
<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>
''Fortunately, writing the integral as a residue in the last line fixes the problem.''
==Applications==
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