We will now derive two results based on Cauchy's Residue Theorem. They have important practical applications and pertain only to functions all of whose isolated singularities are poles. Definition 8.1, Page 274. Observe that analytic functions are a special case of meromorphic functions. Theorem 8.8, Page 274.
C be a simple closed positively oriented contour in D along which .
Corollary 8.1, Page 275. C be a simple closed positively oriented contour in D along which . Theorem 8.9, Page 275. Proof of Theorem 8.9, see text Page 275. Example 8.22, Page 276.