I need some help with the question attached.
It's my understanding that an analytic function is differentiable at every point in the domain.
What does "nowhere analytic" mean. Is the premise behind this question that the function is differentiable on the coordinate (does coordinate mean real?) axes and not differentiable on the imaginary axes?
OR, is it that, there is some point where the function is differentiable, but it is not an entire function?
i found the C-R Equations.
du/dx = 3x^2 + 3y^3 -3 , dv/dy = 3y^2 - 2 + 3x^2
du/dy = 6xy , dv/dx = 6xy
du/dx = dv/dy
and du/dy = - dv/dx where x = 0 or y = 0
and thus C-R equations are not satisfied on an open disk, but only on the line x=0 or y=0
I think this is wrong.
Any help appreciated, especially if you point out the thought process required here.