ellipj(u, m) = <ufunc 'ellipj'>¶
Jacobian elliptic functions
Calculates the Jacobian elliptic functions of parameter m between 0 and 1, and real argument u.
- sn, cn, dn, phndarrays
The returned functions:
sn(u|m), cn(u|m), dn(u|m)
The value ph is such that if u = ellipkinc(ph, m), then sn(u|m) = sin(ph) and cn(u|m) = cos(ph).
Wrapper for the Cephes  routine ellpj.
These functions are periodic, with quarter-period on the real axis equal to the complete elliptic integral ellipk(m).
Relation to incomplete elliptic integral: If u = ellipkinc(phi,m), then sn(u|m) = sin(phi), and cn(u|m) = cos(phi). The phi is called the amplitude of u.
Computation is by means of the arithmetic-geometric mean algorithm, except when m is within 1e-9 of 0 or 1. In the latter case with m close to 1, the approximation applies only for phi < pi/2.