Jacobi elliptic functions
= Jacobi elliptic functions
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The Jacobi elliptic functions include $\operatorname{sn}(u,k)$, $\operatorname{cn}(u,k)$ and $\operatorname{dn}(u,k)$, with $\operatorname{sn}^2+\operatorname{cn}^2=1$ and $\operatorname{dn}^2+k^2\operatorname{sn}^2=1$. Their ratios give the other standard members. The <Jacobi elliptic sine> is the inverse of the <elliptic integral of the first kind>.