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:
- uarray_like
- Argument. 
- marray_like
- Parameter. 
- 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- phiis 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/