留数计算方法

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.