Complex differentiability problem

[Epsilon36819]

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!

 

[tiny-tim]

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!

 

[Epsilon36819]

That does make sense. I really did read this as "a non zero" derivative...

Thanks for clearing that up!