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# Contour Integral

An integral obtained by contour integration. The particular path in the complex plane used to compute the integral is called a contour.

As a result of a truly amazing property of holomorphic functions, a closed contour integral can be computed simply by summing the values of the complex residues inside the contour.

Watson (1966 p. 20) uses the notation to denote the contour integral of with contour encircling the point once in a counterclockwise direction.

Renteln and Dundes (2005) give the following (bad) mathematical joke about contour integrals:

Q: What's the value of a contour integral around Western Europe? A: Zero, because all the Poles are in Eastern Europe.

Contour, Contour Integration, Definite Integral, Integral, Path Integral, Pole, Riemann Integral

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## References

Renteln, P. and Dundes, A. "Foolproof: A Sampling of Mathematical Folk Humor." Notices Amer. Math. Soc. 52, 24-34, 2005.Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1966.

Contour Integral

## Cite this as:

Weisstein, Eric W. "Contour Integral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ContourIntegral.html