# Dictionary:Cauchy-type integral

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The function at a point z0 within a closed contour C can be expressed in terms of a line integral along C if f(z) is a continuous analytic function:

${\displaystyle f(a)={\frac {1}{2\pi i}}\oint {\frac {f(z)}{z-z_{0}}}dz}$.

Named for Augustin Louis Cauchy (1789–1857), French mathematician.

See Cauchy integral formula for more information.