456 Chapter^7
c
Fig. 7.1:~
The points A' and H divide the contour C into two arcs C' and C",
both with the. same orientation as C, so that C = C' + C". Simi-
larly, the points B ·and D divide the contour C1 into two arcs Ci and
Cf which we will consider as described in the negative direction (as in-
dicated by arrows in Fig. 7.12), so that C 1 = -Ci - Cf^1 • In the same
manner we have C 2 = -C~ - C~^1 • Next, we consider the two simple closed
contours
r
1= c
1- 'Ya + c~ - 'Yz + c~ -'Y1
r'
1= 'Y1 + c~
1
+ 'Y2 + q' + 1a + c"and note that (r^1 ) c G, Int(r') c R c G, and similarly for r^11 •
Since f is analytic on and within each of the contours r^1 and r^11 , we
have, by Corollary 7.13,