Given the integrals of the form
To convert it to a complex integral on , we parametrize the contour by . We can then write
i.e.
Then ^09155cEquation (1) becomes
where is the unit circle .
Cauchy principal value of an integral is defined by
If a integral diverges, it may still possess a Cauchy principal value.
Another powerful lemma is ^3910a9Lemma 2 (Jordan's Lemma).
Next we calculate
Indented contour is of great use.