- #1

MathLearner123

- 16

- 3

Why the function ##g(w)## is well-defined on ##\mathbb{D} \setminus \{0\}##? I don't understand how ##\log## function works here and how a branch of ##\log## function can be defined on whole ##\mathbb{D} \setminus \{0\}##. For example principal branch of logarithm is defined on ##\mathbb{C} \setminus \mathbb{R}_{-}## so can not be used for ##\mathbb{D} \setminus \{0\}##. Thanks!