Semicircular contour: Difference between revisions
(New page: ==Definition== A '''semicircular contour''' of radius <math>R</math> is a contour comprising: * A semicircle of radius <math>R</math>, centered at the origin, and in the upper half-plane...) |
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A '''semicircular contour''' of radius <math>R</math> is a contour comprising: | A '''semicircular contour''' of radius <math>R</math> is a contour comprising: | ||
* A semicircle of radius <math>R</math>, centered at the origin, and in the upper half-plane | * A semicircle of radius <math>R</math>, centered at the origin, and in the [[upper half-plane]] | ||
* The diameter of this semicircle, joining the points <math>R</math> and <math>-R</math> | * The diameter of this semicircle, joining the points <math>R</math> and <math>-R</math> | ||
Semicircular contours are often used to compute integrals along the real line; for this, we take the limit as <math>R \to \infty</math>. {{further|[[semicircular contour integration method]]}} | Semicircular contours are often used to compute integrals along the real line; for this, we take the limit as <math>R \to \infty</math>. {{further|[[semicircular contour integration method]]}} | ||
Revision as of 19:12, 1 May 2008
Definition
A semicircular contour of radius is a contour comprising:
- A semicircle of radius , centered at the origin, and in the upper half-plane
- The diameter of this semicircle, joining the points and
Semicircular contours are often used to compute integrals along the real line; for this, we take the limit as .
- Further information: semicircular contour integration method