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 int^((a+))f(z)dz to denote the contour integral of f(z) with contour encircling the point a 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.

See also

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.

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Contour Integral

Cite this as:

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

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