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

Did you compute $\displaystyle \frac{g(z)g(z_0)}{zz_0}$ for $\displaystyle z,z_0\in\mathbb C\setminus \overline D$ ?

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

Yes, we try to check the definition of holomorphic.

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.