2
votes
0answers
23 views

Proof that function is real part of $\sec(z)$ [duplicate]

I'm working on the following problem: I've deduced that the key is to show that $u$ is the real part of $\sec(z)$. But, I'm getting stuck in the algebra and am hoping someone can point me in the ...
1
vote
1answer
311 views

Derive Poisson's integral formula for Im z>0

How to derive Poisson's integral formula for $\text{Im }{z}>0$ given that for $|z|<1 $ we have ...
2
votes
1answer
144 views

Harmonic function with bounded preimage

I recently saw a question here about bounded/unbounded preimages of a set under a harmonic function. The question asked did not seem to make sense as it was talking about harmonic functions on ...