294 CHAPTER 8 • RESIDUE THEORY
Figure 8.1 The domain D and contour C and the singular points z 1 , zz, ... , z,. in the
statement of Cauchy's residue theorem.
expansion, we seek a method to calculate the residue from special information
about the nature of the singularity at zo.
If f has a removable singularity at zo, then <l-n = 0, for n = 1, 2, ....
Therefore, Res[f, zo] = O. Theorem 8.2 gives methods for evaluating residues at
poles.