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Homework Help: Harmonic Functions(HELP )

  1. Oct 12, 2005 #1
    Harmonic Functions(HELP!!!!)

    Could someone please help me with this proof.

    Show that if O(x,y) is harmonic, then Ox - iOy is analytic(you may assume that O has continuous partial derivatives of all orders.)

    How would I go about solving this.
  2. jcsd
  3. Oct 12, 2005 #2
    what's the definition of a harmonic function?

    what's the definition of an analytic function (rather, how do you judge if a function is analytic--ie, cauchy-riemann equations)?

    so start with supposing that your function is harmonic.

    then try and show that your function must also satisfy the cauchy-riemann equations for all x and y.
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