\[\operatorname{sn}\left(z,k\right)=\frac{(1+k_{2}^{\prime})\operatorname{sn}%
\left(z/(1+k_{2}^{\prime}),k_{2}\right)\operatorname{cn}\left(z/(1+k_{2}^{%
\prime}),k_{2}\right)}{\operatorname{dn}\left(z/(1+k_{2}^{\prime}),k_{2}\right%
)},\]