Recall that if and , (see def open ball). As we work in the plane, it can happen that this open ball is also called an open disk.
Another formulation of the above formula is as follows:
The denominator vanishes at two points, and , both inside the contour. We will decompose this contour into two Jordan curves by the following way: draw the diameter of the circle which coincides with the x-axis. Denote:
Then (the variable ``travels'' twice on the diameter, but in opposite directions).
Therefore we have:
Noah Dana-Picard 2007-12-24