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Math Help - show harmonic by representing by composition of maps

  1. #1
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    show harmonic by representing by composition of maps

    show tan^{-1}(\frac{2x}{x^{2}+y^{2}-1}) is harmonic by considering  h(w(z))=log(\frac{i+z}{i-z})


    i found that h(w(z)) is just the same as the function required. but how can i show it is harmonic by writing it as composition of maps?
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  2. #2
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    Quote Originally Posted by szpengchao View Post
    show tan^{-1}(\frac{2x}{x^{2}+y^{2}-1}) is harmonic by considering  h(w(z))=log(\frac{i+z}{i-z})


    i found that h(w(z)) is just the same as the function required. but how can i show it is harmonic by writing it as composition of maps?
    Remember that the real and imaginary parts of an analytic function on an open set S are harmonic on S.
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