\[\operatorname{dc}\left(2z,k\right)=\frac{{\operatorname{dc}}^{2}\left(z,k%
\right)+{k^{\prime}}^{2}{\operatorname{sc}}^{2}\left(z,k\right){\operatorname{%
nc}}^{2}\left(z,k\right)}{1-{k^{\prime}}^{2}{\operatorname{sc}}^{4}\left(z,k%
\right)},\]