Integral symbol for closed loops over functions?

1. Jan 18, 2014

jackmell

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 $\pi/12$ 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. Jan 18, 2014

SteamKing

Staff Emeritus
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.