Contour integration
Method of evaluating certain integrals along paths in the complex plane / From Wikipedia, the free encyclopedia
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This article is about the line integral in the complex plane. For the general line integral, see Line integral.
In the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane.[1][2][3]
Contour integration is closely related to the calculus of residues,[4] a method of complex analysis.
One use for contour integrals is the evaluation of integrals along the real line that are not readily found by using only real variable methods.[5]
Contour integration methods include:
- direct integration of a complex-valued function along a curve in the complex plane;
- application of the Cauchy integral formula; and
- application of the residue theorem.
One method can be used, or a combination of these methods, or various limiting processes, for the purpose of finding these integrals or sums.