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Module « scipy.special »

Fonction ellipkm1 - module scipy.special

Signature de la fonction ellipkm1

def ellipkm1(*args, **kwargs) 

Description

help(scipy.special.ellipkm1)

ellipkm1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    ellipkm1(p, out=None)

    Complete elliptic integral of the first kind around `m` = 1

    This function is defined as

    .. math:: K(p) = \\int_0^{\\pi/2} [1 - m \\sin(t)^2]^{-1/2} dt

    where `m = 1 - p`.

    Parameters
    ----------
    p : array_like
        Defines the parameter of the elliptic integral as `m = 1 - p`.
    out : ndarray, optional
        Optional output array for the function values

    Returns
    -------
    K : scalar or ndarray
        Value of the elliptic integral.

    See Also
    --------
    ellipk : Complete elliptic integral of the first kind
    ellipkinc : Incomplete elliptic integral of the first kind
    ellipe : Complete elliptic integral of the second kind
    ellipeinc : Incomplete elliptic integral of the second kind
    elliprf : Completely-symmetric elliptic integral of the first kind.

    Notes
    -----
    Wrapper for the Cephes [1]_ routine `ellpk`.

    For ``p <= 1``, computation uses the approximation,

    .. math:: K(p) \\approx P(p) - \\log(p) Q(p),

    where :math:`P` and :math:`Q` are tenth-order polynomials.  The
    argument `p` is used internally rather than `m` so that the logarithmic
    singularity at ``m = 1`` will be shifted to the origin; this preserves
    maximum accuracy.  For ``p > 1``, the identity

    .. math:: K(p) = K(1/p)/\\sqrt(p)

    is used.

    References
    ----------
    .. [1] Cephes Mathematical Functions Library,
           http://www.netlib.org/cephes/
    

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