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Module « scipy.special »

Fonction ellipk - module scipy.special

Signature de la fonction ellipk

def ellipk(*args, **kwargs) 

Description

help(scipy.special.ellipk)

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


    ellipk(m, out=None)

    Complete elliptic integral of the first kind.

    This function is defined as

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

    Parameters
    ----------
    m : array_like
        The parameter of the elliptic integral.
    out : ndarray, optional
        Optional output array for the function values

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

    See Also
    --------
    ellipkm1 : Complete elliptic integral of the first kind around m = 1
    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
    -----
    For more precision around point m = 1, use `ellipkm1`, which this
    function calls.

    The parameterization in terms of :math:`m` follows that of section
    17.2 in [1]_. Other parameterizations in terms of the
    complementary parameter :math:`1 - m`, modular angle
    :math:`\sin^2(\alpha) = m`, or modulus :math:`k^2 = m` are also
    used, so be careful that you choose the correct parameter.

    The Legendre K integral is related to Carlson's symmetric R_F
    function by [2]_:

    .. math:: K(m) = R_F(0, 1-k^2, 1) .

    References
    ----------
    .. [1] Milton Abramowitz and Irene A. Stegun, eds.
           Handbook of Mathematical Functions with Formulas,
           Graphs, and Mathematical Tables. New York: Dover, 1972.
    .. [2] NIST Digital Library of Mathematical
           Functions. http://dlmf.nist.gov/, Release 1.0.28 of
           2020-09-15. See Sec. 19.25(i) https://dlmf.nist.gov/19.25#i
    

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