scipy.special.ellipj#
- scipy.special.ellipj(u, m, out=None) = <ufunc 'ellipj'>#
Jacobian elliptic functions
Calculates the Jacobian elliptic functions of parameter m between 0 and 1, and real argument u.
- Parameters:
- marray_like
Parameter.
- uarray_like
Argument.
- outtuple of ndarray, optional
Optional output arrays for the function values
- Returns:
- sn, cn, dn, ph4-tuple of scalar or ndarray
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).
See also
Notes
Wrapper for the Cephes [1] 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.
References
[1]Cephes Mathematical Functions Library, http://www.netlib.org/cephes/