Jacobi elliptic sine
= Jacobi elliptic sine
{c}
{title2=$\operatorname{sn}(u,k)$}
The Jacobi elliptic sine is the local inverse of the <elliptic integral of the first kind>: if
$$
u=\int_0^z\frac{dt}{\sqrt{(1-t^2)(1-k^2t^2)}},
$$
then $z=\operatorname{sn}(u,k)$. Its analytic continuation is a meromorphic doubly periodic function.
It is the sn member of the <Jacobi elliptic functions>.