Show that \(f\) is holomorphic iff \(\delbar f = 0\).
Solution
\[ 2\delbar f &\da (\del_x + i \del_y) (u+iv) \\ &= u_x + iv_x + iu_y - v_y \\ &= (u_x - v_y) + i(u_y + v_x) \\ &= 0 && \text{by Cauchy-Riemann} .\]
Holomorphic iff delbar vanishes
E-P2PEF
- Area
- Complex Analysis
- Topics
- Cauchy-Riemann, Holomorphic Functions
- Status
- draft