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Can anyone tell me how to calculate the Poisson kernel for the upper half plane? I am able to calculate it for the unit disc and I know the unit disc and the upper half plane are conformally equivalent, do I need this?

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    You probably don't need this, but I'd probably try to use the [Cayley-transform](http://en.wikipedia.org/wiki/Cayley_transform#Conformal_map) to guess the Poisson kernel for the upper half plane. If you get the formula right, then it should be possible to derive it without resorting to the unit disk, but I don't quite see the point (and I haven't checked). *Added:* Actually [Wikipedia seems to answer this question](http://en.wikipedia.org/wiki/Poisson_kernel#On_the_upper_half-plane). Could you please try and be a bit more precise what exactly you're asking? I must say that I'm a bit confused.2011-05-12

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