This is again for an old exam.
Let $f$ be an entire function, show that f(z)f(1/z) is entire.
How do I go about showing the above.
Do I use the definition of analyticity?., Call g: f(z)f(1/z) and show that it is complex differentiable everywhere?
Edit: Well the original question was.
Let $f$ be entire and suppose $f(z)f(1/z)$ is bounded on $\mathbb C$, then $f(z)=az^n$ for some $a\in \mathbb C$.
I was trying to show that $f(z)f(1/z)$ is entire and then use Louiville's theorem. :). I hope this makes sense.