I have noticed through tinkering in Mathematica that this particular combination of theta functions of nome $e^{-\pi}$ is periodic and looks alot like cosine. Is there any identity I can use to realize a simpler form?
$\frac{(\theta_4(ix/2))^2 \exp(-x^2/4\pi)}{ \theta_3(ix/2)}$
Here x is a real variable.
Alternatively, if it's not easily simplified, how would I calculate it's Fourier series coefficients. 