I am new to using these functions and am confused about what is a function of what.
If I want to solve $sn(x,k)$ for a given x, and use this equation: $sn(u,k)=\frac{\theta_{2}}{\theta _{3}}\frac{\theta _{1}(u\theta _{3}^{-2})}{\theta _{4}(u\theta _{3}^{-2})}$ , would $\theta _{2}$ and $\theta _{3}$ in the equation mean $z=0$ and $q=u=x$ in the definitions of the theta functions i.e. $\theta_{2}(z,q)\equiv \sum_{n=-\infty }^{\infty }q^{(n+1/2)^{2}}e^{(2n+1)iz}$?
And similarly, would $\theta _{1}(u\theta _{3}^{-2})$ mean that $z=0$ and $q=u\theta _{3}^{-2}$ (where $u=x$)?