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Slightly adjusted notation.
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This commit is contained in:
Bokuan Li
2026-05-31 23:20:08 -04:00
parent 5cf2bd9f10
commit 639aa253cf
1 changed files with 1 additions and 1 deletions
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src/dg/complex/runge.tex
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@@ -9,7 +9,7 @@
\[ \[
f(z_0) = \frac{1}{2\pi i}\sum_{j = 1}^n \int_{\gamma_j} \frac{f(z)}{z - z_0}dz f(z_0) = \frac{1}{2\pi i}\sum_{j = 1}^n \int_{\gamma_j} \frac{f(z)}{z - z_0}dz
\] \]
\item For every $V \in \cn_\complex(U)$, $f \in H(V; E)$, and $z_0 \in V \setminus U$, \item For every $W \in \cn_\complex(U)$, $f \in H(W; E)$, and $z_0 \in W \setminus U$,
\[ \[
\frac{1}{2\pi i}\sum_{j = 1}^n \int_{\gamma_j} \frac{f(z)}{z - z_0}dz = 0 \frac{1}{2\pi i}\sum_{j = 1}^n \int_{\gamma_j} \frac{f(z)}{z - z_0}dz = 0
\] \]