estimating theorem of contour integral


If f is a continuous complex function on the rectifiable curve γ of the complex planeMathworldPlanetmath, then

|γf(z)𝑑z|maxzγ|f(z)|l, (1)



is the of γ.

The form of (1) concerning the continuous real function f on the intervalMathworldPlanetmathPlanetmath [a,b] is


For applications of this important theorem, see the example of using residue theoremMathworldPlanetmath.

Title estimating theorem of contour integral
Canonical name EstimatingTheoremOfContourIntegral
Date of creation 2013-03-22 15:19:36
Last modified on 2013-03-22 15:19:36
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 7
Author pahio (2872)
Entry type Theorem
Classification msc 30E20
Classification msc 30A99
Synonym estimation theorem of integral
Synonym integral estimating theorem
Related topic MinimalAndMaximalNumber
Related topic AnalyticContinuationOfRiemannZetaUsingIntegral
Related topic IntegralMeanValueTheorem