\[\frac{\theta_{1}\left(z,q\right)\theta_{2}\left(z,q\right)}{\theta_{1}\left(2z%
,q^{2}\right)}=\frac{\theta_{3}\left(z,q\right)\theta_{4}\left(z,q\right)}{%
\theta_{4}\left(2z,q^{2}\right)}=\theta_{4}\left(0,q^{2}\right),\]