\[\operatorname{sc}\left(z,k\right)=\frac{\theta_{3}\left(0,q\right)}{\theta_{4}%
\left(0,q\right)}\frac{\theta_{1}\left(\zeta,q\right)}{\theta_{2}\left(\zeta,q%
\right)}=\frac{1}{\operatorname{cs}\left(z,k\right)}.\]