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, PoleExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Contour." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Contour.html