1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

308 CHAPTER 8 • RESIDUE THEORY

If f (x) = ~~:j, where P and Qare polynomials, then f is called a rational

function. In calculus you probably learned techniques for integrating certain
types of rational functions. We now show how to use the residue theorem to
obtain the Cauchy principal value of the integral of Jover (- 00 ,00).

y

R

Figure 8.4 T he poles z1, z2, ... , Zk-1, zk of G that lie in the upper half-plane.