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B Partial derivative of the harmonic complex function

  1. Jun 17, 2016 #1
    For a harmonic function of a complex number ##z##, ##F(z)=\frac{1}{z}##, which can be put as ##F(z)=f(z)+g(\bar{z})##and satisfies ##\partial_xg=i\partial_yg##. But this function can also be put as ##F(z)=\frac{\bar{z}}{x^2+y^2}## which does not satisfy that derivative equation!

    Sorry, I should have put this thread in homework section.
     
    Last edited: Jun 17, 2016
  2. jcsd
  3. Jun 18, 2016 #2

    Svein

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    Actually, if F is analytic, [itex]\frac{\partial F}{\partial\bar{z}}=0[/itex].
     
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