We are following the notation in Complex Variables and Applications (Brown and Churchill).
The method of using complex analysis to evaluate integrals is to consider a very large semicircular region’s boundary, which consists of the segment of the real axis from to and the top half of the circle positively oriented is denoted by .
. If , then . Furthermore if is even, then .
Let two functions and be analytic at a point . If , and , then is a simple pole of the quotient and .