be a function, analytic at all the interior points of a Jordan curve
a finite number of isolated singular points
is oriented in the positive direction.
- Only the interior singularities are involved.
We wish to compute the integral
The function has a pole of order 1 at
, a pole of order 2 at1 and a pole of order 3 at 3; this last pole is irrelevant to our computation as it lies out of the Jordan curve defined by
. So we compute two residues:
Compute the integral
We use 2.1:
The denominator has two complex roots
. Only the second one is
a point interior to the unit-circle, i.e. it is the only pole of the function we have to deal with. Therefore: