Solution

Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 8 / 3 / Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 13E / c / Solution

{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>.

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 Incoming links: Jacobi elliptic sine