Category:Cauchy's Residue Theorem
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This category contains pages concerning Cauchy's Residue Theorem:
Let $U$ be a simply connected open subset of the complex plane $\C$.
Let $a_1, a_2, \dots, a_n$ be finitely many points of $U$.
Let $f: U \to \C$ be analytic in $U \setminus \set {a_1, a_2, \dots, a_n}$.
Let $L$ be a contour in $\C$ oriented anticlockwise.
Let $\partial U_k$ denote the closed contour bounding $U_k$.
Then:
- $\ds \oint_L \map f z \rd z = 2 \pi i \sum_{k \mathop = 1}^n \Res f {a_k}$
where $\Res f {a_k}$ denotes the residue at $a_k$ of $f$.
Source of Name
This entry was named for Augustin Louis Cauchy.
Subcategories
This category has only the following subcategory.
Pages in category "Cauchy's Residue Theorem"
The following 2 pages are in this category, out of 2 total.