Define \[ f(z)= \begin{cases} e^{-1/z^4},&z\ne0,\\ 0,&z=0. \end{cases} \] The source states that \(f\) satisfies the Cauchy–Riemann equations at every point of \(\mathbb C\) but is not analytic. Explain how this is possible.
Cauchy–Riemann equations everywhere do not imply analyticity
P-WESCA04-E2
- Area
- Complex Analysis
- Seen at
- WESLEYAN
- Years
- 2004
- Status
- draft