Prove that if \(D\) is a simply connected domain and \(f(z)\) is holomorphic and nonzero on \(D\), then \(f(z)=e^{g(z)}\), where \(g(z)\) is holomorphic on \(D\).
Solution
A nowhere-vanishing holomorphic function on a simply connected domain is of the form $e^g$
P-Y5SS5
- Area
- Complex Analysis
- Topics
- Complex Logarithm, Holomorphic Functions
- Status
- draft