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Complex differentiability problem

  1. Mar 12, 2008 #1
    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?

  2. jcsd
  3. Mar 12, 2008 #2


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    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:
  4. Mar 12, 2008 #3
    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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