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Integral symbol for closed loops over functions?

  1. Jan 18, 2014 #1
    I find it sometimes confusing dealing with integrals of multi-valued functions in distinguishing a closed integration path, and an integration path which forms a closed loop over the function. They can of course be quite different. For example:

    $$\oint f(z)dz.$$

    Now, is the integration to be done simply over any of the multiple sheets, for example random every [itex]\pi/12[/itex] over a circle or, is the integration to be done over an analytically-continuous path over the function?

    Why don't we have a special integral symbol for the later?
    Last edited: Jan 18, 2014
  2. jcsd
  3. Jan 18, 2014 #2


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    Usually, the particular path of the integral will be described somewhere, either in text accompanying the integral or with some mathematical notation. Not all path integrals are necessarily evaluated over a circular, or even a curved, path.
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