Quote:
Originally Posted by Liav Teichner  I need to decide whether the following statement is true or not:
let f be a complex function, f(z)=f(x+iy)=u(x,y)+iv(x,y).if u and v satisfy the Cauchy-Riemann equations in a neighborhood of z_0 then f is differentiable at z_0. |
no. consider
, where
,
and consider the derivative at z_0 = 0
i got this example from a text book.
can you come up with a nicer example, TPH?