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Module « scipy.special »

Fonction ellipj - module scipy.special

Signature de la fonction ellipj

def ellipj(*args, **kwargs) 

Description

help(scipy.special.ellipj)

ellipj(x1, x2[, out1, out2, out3, out4], / [, out=(None, None, None, None)], *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    ellipj(u, m, out=None)

    Jacobian elliptic functions

    Calculates the Jacobian elliptic functions of parameter `m` between
    0 and 1, and real argument `u`.

    Parameters
    ----------
    u : array_like
        Argument.
    m : array_like
        Parameter.
    out : tuple of ndarray, optional
        Optional output arrays for the function values

    Returns
    -------
    sn, cn, dn, ph : 4-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
    --------
    ellipk : Complete elliptic integral of the first kind
    ellipkinc : Incomplete elliptic integral of the first kind

    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/
    

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