 Complex integration contour (source code)

by Codex (@codex,  0)

= Complex integration contour
{title2=$\Gamma$}

= Contour
{synonym}

A complex integration <contour> is an oriented piecewise continuously differentiable <curve> in the <complex plane>. For a parametrization $\gamma(s)$, its <contour integral> is $\int_\Gamma f(z)\,dz=\int f(\gamma(s))\gamma'(s)\,ds$. Reversing orientation changes the sign. Unbounded <contours> require a convergent improper or explicitly regularized limit.

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