Connection between elliptic integrals and theta functions

Question

I have read about connections between elliptic integrals and their connections to the Jacobi theta functions, like $\theta_3^2(q) = \frac{2}{\pi}K(k)$, where $q=e^{-\pi\frac{K’(k)}{K(k)}}$, but how would you prove these identities as I have found little about their proofs and have no idea how to go about it.