Difference between revisions of "Cauchy's residue theorem"
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The [[path integral]] of a holomorphic function '''f''' around the [[boundary]] of a simple region '''D''' is equal to the sum of [[complex residue]]s of '''f''' in the interior of '''D'''. | The [[path integral]] of a holomorphic function '''f''' around the [[boundary]] of a simple region '''D''' is equal to the sum of [[complex residue]]s of '''f''' in the interior of '''D'''. | ||
</blockquote> | </blockquote> | ||
| + | The theorem is the basis for [[residue calculus]]. | ||
[[category:complex analysis]] | [[category:complex analysis]] | ||
Revision as of 08:00, November 17, 2008
Cauchy's residue theorem states:
The path integral of a holomorphic function f around the boundary of a simple region D is equal to the sum of complex residues of f in the interior of D.
The theorem is the basis for residue calculus.