Analyticity of the logarithmic function.

Definition 4.5.1   Let $ f$ be a multivalued function. A branch of $ f$ is a single valued function, which is analytic on some domain $ \mathcal{D}$ . At every point of $ \mathcal{D}$ , the value of the branch is exactly one of the multiple values of $ f$ at that point.

Example 4.5.2   The principal part Log of the $ \log$ function is a branch of $ \log$ , defined over $ \mathbb{C}^*$ .

Noah Dana-Picard 2007-12-24