Given is $f(z)=\log(1-\frac{z}{2})$. How do I examine if the function is analytic and calculate the function representation of the function at $z_0=0$?
What I did:
The log function is singular at zero, and only at zero. So my function is analytic except where $z= 2$ as $1 - z/2 = 0$ there. I think this is correct.
But how should I do second part?