# Complex Analysis: Cauchy Integral Formula

1. Apr 29, 2010

### masterslave

1. The problem statement, all variables and given/known data
The problem, for reference, is from Sarason's book "Complex Function Theory, 2nd edition" and is on page 81, Exercise VII.5.1.

Let C be a counterclockwise oriented circle, and let f be a holomorphic function defined in an open set containing C and its interior. What is the value of the Cauchy Integral, $$\int_{C} \frac{f(\zeta)}{\zeta-z} d\zeta$$, when z is in the exterior of C?

2. Relevant equations
The Cauchy Integral formula, as mentioned in the problem.

3. The attempt at a solution
I haven't the slightest how to begin the problem. My intuition, though, tells me $$\int_{C} \frac{f(\zeta)}{\zeta-z} d\zeta=0$$. Any insight is appreciated.

2. Apr 29, 2010

### Dick

If z is in the exterior of C then f(zeta)/(zeta-z) is holomorphic in zeta over all of C.