Example 1 In this example, we consider an unbounded multiply connected region of connectivity 4 bounded by the four circles (see Figure 2).
Figure 1 A bounded multiply connected region Ω of connectivity (pmb{m+1}).
Figure 1 An unbounded multiply connected region G of connectivity m.
We assume that (0notinOmega). Figure 2 An unbounded multiply connected region Ω of connectivity m.
Cauchy's theorem, mentioned above, states that the value of such an integral is the same for two contours C1 and C2, provided both curves lie inside a simply connected region Ω a region with no "holes".
Let ℛ be a simply connected region containing the origin.
Definition 2.1 Let f ( z ) be analytic in a simply connected region ℛ.
Theorem 3.1 Let f ( z ) be an analytic function in a simply connected region ℛ.
Theorem 1 (i) Let ℛ be a simply connected region containing the origin.
Theorem 3 Let f ( z ) be an analytic function in the simply connected region ℛ containing the origin.
Definition 1 Let f ( z ) be analytic in a simply connected region ℛ of the complex z-plane.
