Understanding of Analytic Branch What does it mean for a function ''to have a branch that is analytic''? Can someone give me an example of it as well please?
thanks

Some functions have multiple values, for example $\log z = \log |z| + i(\text{arg } z + 2\pi k)$, $k \in \mathbb{Z}$. Such a function "has an analytic branch" when we can define it to be single valued and analytic. We can do this for the logarithm by restricting the argument to be $-\pi < \theta < \pi$, which is called the principal branch. 
