Looking into the discussion in this post, I was naturally led to consider the following general identity
Given the two well known jacobi theta functions, namely $\theta_2(q)=\sum_{n=-\infty}^\infty q^{(n+1/2)^2}$ and $\theta_3(q)=\sum_{n=-\infty}^\infty q^{n^2}$ where $q=e^{2 \pi i\tau}$, $|q|\lt1$
It is then conjectured that the following identity is true
$\frac{\cfrac{2\,q^{\frac{1}{2}}}{1-q^2+\cfrac{q^2(1-q^2)^2}{1-q^6+\cfrac{q^4(1-q^4)^2}{1-q^{10}+\cfrac{q^6(1-q^6)^2}{1-q^{14}+\ddots}}}}}{\cfrac{1}{1-q+\cfrac{q(1+q)^2}{1-q^3+\cfrac{q^2(1+q^2)^2}{1-q^5+\cfrac{q^3(1+q^3)^2}{1-q^7+\ddots}}}}}=\theta_2(q^2)\,\theta_3(q^2)$