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Contour


Contour

A path in the complex plane over which contour integration is performed to compute a contour integral. When choosing a contour to evaluate an integral on the real line, a contour is generally chosen based on the range of integration and the position of poles in the complex plane. For example, for an integral from -infty to +infty along the real axis, the contour at left could be chosen if the function f had no poles on the real line, and the middle contour could be chosen if it had a pole at the origin. To perform an integral over the positive real axis from 0 to +infty for a function with a pole at 0, the contour at right could be chosen.


See also

Complex Residue, Contour Integral, Contour Integration, Contour Line, Contour Plot, Hankel Contour, Inside-Outside Theorem, Pole

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Cite this as:

Weisstein, Eric W. "Contour." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Contour.html

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