# Math Help - Holomorphic function

1. ## Holomorphic function

Hey who can help me with this:
Let f be holomorphic in a neighborhood of a closed disk $\bar{D}$. Then $g(z) = \int_{\delta D}\frac{f(\zeta)d\zeta}{\zeta -z}$ is a holomorphic function on $\mathbb{C}-\bar{D}$.
Why, and which one?

2. Did you compute $\frac{g(z)-g(z_0)}{z-z_0}$ for $z,z_0\in\mathbb C\setminus \overline D$ ?

3. Why do I do this, to check whether its holomorphic?

4. Yes, we try to check the definition of holomorphic.

5. Im somehow lost, when I compute the quotient I just get f'(z) multiplied by a constant. And I dont really use the fact that z is outside D.