Theorem 6.7 (Extended Cauchy-Goursat Theorem).  Let     be simple closed positively oriented contours with the property that    lies interior to C for     and the set of interior to    has no points in common with the set interior to    if  .  Let  f(z)  be analytic on a domain D that contains all the contours and the region between C and  ,  as shown in Figure 6.26. Then

            .  

 

Figure 6.26  The multiply connected domain D and the contours    in the statement of the extended Cauchy-Goursat theorem.

Proof.

Proof of Theorem 6.7 is in the book.

Complex Analysis for Mathematics and Engineering