Complex differentiability problem

Main Question or Discussion Point

Hi guys,

I have this problem understanding that holomorpic functions must be infinitely differentiable. Indeed, it does follow from the Cauchy formula. But take z=x+iy. It satisfies C-R equations and has a first derivative = 1. I fail to see how this function is infinitely differentiable.

What am I missing?

Thanks!
 

Answers and Replies

tiny-tim
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But take z=x+iy. It satisfies C-R equations and has a first derivative = 1.
So its second derivative is 0.

And its third, and its fourth, and …

Being (infinitely) differentiable simply means that it has a derivative - the derivative doesn't have to be non-zero.

It's like, is zero a number? You could say it's not anything, so it's not a number … but it is!! :smile:
 
That does make sense. I really did read this as "a non zero" derivative...:redface:

Thanks for clearing that up! :smile:
 
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