show harmonic by representing by composition of maps

**szpengchao** · February 10th 2009, 11:34 PM

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?

**ThePerfectHacker** · February 11th 2009, 02:50 PM

Originally Posted by szpengchao

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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