So I was snooping around Proof Wiki for the Poisson Summation Formula proof and came across this:
https://proofwiki.org/wiki/Poisson_Summation_Formula
In the end it makes the statement:
Therefore by the definition of the Fourier series of $\space f \space$ :
$F(x) = \sum_{k \in \mathbb{Z}} \hat{f}(x)e^{ikx}$
Is it not $\space \hat{f}(x)e^{ik2\pi x}$?
Or am I missing something?