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-rw-r--r--pages/complex-analysis/one-complex-variable/the-calculus-of-residues.md36
1 files changed, 13 insertions, 23 deletions
diff --git a/pages/complex-analysis/one-complex-variable/the-calculus-of-residues.md b/pages/complex-analysis/one-complex-variable/the-calculus-of-residues.md
index b49cdf4..a2fa53d 100644
--- a/pages/complex-analysis/one-complex-variable/the-calculus-of-residues.md
+++ b/pages/complex-analysis/one-complex-variable/the-calculus-of-residues.md
@@ -3,16 +3,13 @@ title: The Calculus of Residues
parent: One Complex Variable
grand_parent: Complex Analysis
nav_order: 4
-# cspell:words
-#published: false
---
# {{ page.title }}
-{: .definition-title }
-> Definition (Residue)
->
-> TODO
+{% definition Residue %}
+TODO
+{% enddefinition %}
Calculation of Residues
@@ -32,24 +29,17 @@ $$
\Res(f,c) = \frac{g(c)}{h'(c)}
$$
+{% theorem * Residue Theorem (Basic Version) %}
+Let $f$ be a function meromorphic in an open subset $G \subset \CC$.
+Let $\gamma$ be a contour in $G$ such that
+the interior of $\gamma$ is contained in $G$
+and contains finitely many poles $c_1, \ldots, c_n$ of $f$.
+Then
-
-
-{: .theorem-title }
-> Residue Theorem (Basic Version)
-> {: #residue-theorem-basic-version }
->
-> Let $f$ be a function meromorphic in an open subset $G \subset \CC$.
-> Let $\gamma$ be a contour in $G$ such that
-> the interior of $\gamma$ is contained in $G$
-> and contains finitely many poles $c_1, \ldots, c_n$ of $f$.
-> Then
->
->
-> $$
-> \int_{\gamma} f(z) \, dz = 2 \pi i \sum_{k=1}^n \Res(f,c_k)
-> $$
-> {: .katex-display .mb-0 }
+$$
+\int_{\gamma} f(z) \, dz = 2 \pi i \sum_{k=1}^n \Res(f,c_k)
+$$
+{% endtheorem %}
{% proof %}
{% endproof %}