A complex function that is harmonic but not analytic

Question

Can someone give a simple example of a complex function that is harmonic but not analytic?

Thanks.

D.

Natural examples are $\mbox{Re};z, \mbox{Im}; z, \bar{z}$... — Julien, Mar 02 '13 at 20:35

score 15 · Answer 1 · answered Mar 02 '13 at 20:18

15

$x{}{}{}{}{}{}{}{}{}{}{}{}{}{}$

answered Mar 02 '13 at 20:18

Georges Elencwajg

2

You probably mean $z\mapsto\mathrm{Re}(z)$. – Philippe Malot Mar 02 '13 at 20:20
5

Sorry, couldn't resist the temptation of a one- typographical-character answer :-) [But made it community wiki]. – Georges Elencwajg Mar 02 '13 at 20:20
@girianshiido: yes. – Georges Elencwajg Mar 02 '13 at 20:24
2

Must be a French thing... :-) – Martin Mar 02 '13 at 20:57
@Martin: oui! (and thanks for the link to my predecessors-rivals: grrr...!) – Georges Elencwajg Mar 02 '13 at 21:43
Why didn't you add the links yourself, one wonders? – Did Sep 14 '17 at 14:11

1 Answers1