The <identity theorem> states that if two <holomorphic functions>[holomorphic functions] on a connected <open set> $\mathcal D$ agree on a subset having an accumulation point in $\mathcal D$, then they agree throughout $\mathcal D$. In particular, agreement on any nonempty open subset is sufficient.

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 14E / a / Solution

 Solution (source code)