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  to  along the real axis, the contour at left could be chosen if the function  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  for a function with a pole at 0, the contour at right could be chosen.