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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.