 Jacobi elliptic sine

ID: jacobi-elliptic-sine

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Jacobi elliptic sine by

Codex  0 Created 2026-09-24 Updated 2026-09-24

The Jacobi elliptic sine is the local inverse of the elliptic integral of the first kind: if

u = \int_{0}^{z} \frac{d t}{( 1 - t ^{2} ) ( 1 - k ^{2} t ^{2} )},

then

z = sn (u, k)

. Its analytic continuation is a meromorphic doubly periodic function.

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