Help finding the output for input with conditions I'm trying to find the output where $h[n]$ is the impulse response of a real stable causal LTI system, and $s_0 \epsilon \mathbb{R}$, and where the input is $x[n] = e^{2\pi i n s_0}$ for $n \epsilon \mathbb{N}$.  Supposedly my answer should be a compact formula with no infinite sums...

So since since my system is causal I obtain, $y[k] = e^{2\pi i ks_0}\sum_{n=0}^{\infty}h[n]e^{-2\pi i ns_0}$.  From here I can conclude that since the system is stable this series converges, but without knowing more information about $h[n]$ I can't see any way to further simplify the expression and rid myself of this infinite sum.  Of course I also know by assumption that $y[k],s_0 \epsilon \mathbb{R}$, but I can't see anyway to use this fact without, again, knowing more about $h[n]$.  

I suppose my sum is looking a lot like the standard Fourier transform but I don't see how I can use that with out, once again, knowing more about $h[n]$.  Hopefully someone can help me here, thanks.

Edit: Could it be that a real system implies that $h[n]$ is real?  Although that's still not enough info to allow me to find a closed form for this series.

Edit 2: Or could "real" in this context be referring to a system which is actually implemented?
So since since my system is causal I obtain, $y[k] = e^{2\pi i ks_0}\sum_{n=0}^{\infty}h[n]e^{-2\pi i ns_0}$.  From here I can conclude that since the system is stable this series converges, but without knowing more information about $h[n]$ I can't see any way to further simplify the expression and rid myself of this infinite sum.  


Hint:  The function (of $z$) defined by $\sum_n h[n]z^{-n}$ is given a special
name and is of some importance in signal-processing circles. Do you know about
this function?
What is the value of this function at $z = e^{2 \pi i s_0}$? which by the way
lies on the unit circle in the complex plane, seeing as how we are talking of circles.