Module « scipy.special »

Fonction roots_legendre - module scipy.special

Signature de la fonction roots_legendre

def roots_legendre(n, mu=False) 

Description

roots_legendre.__doc__

Gauss-Legendre quadrature.

    Compute the sample points and weights for Gauss-Legendre
    quadrature. The sample points are the roots of the nth degree
    Legendre polynomial :math:`P_n(x)`. These sample points and
    weights correctly integrate polynomials of degree :math:`2n - 1`
    or less over the interval :math:`[-1, 1]` with weight function
    :math:`w(x) = 1.0`. See 2.2.10 in [AS]_ for more details.

    Parameters
    ----------
    n : int
        quadrature order
    mu : bool, optional
        If True, return the sum of the weights, optional.

    Returns
    -------
    x : ndarray
        Sample points
    w : ndarray
        Weights
    mu : float
        Sum of the weights

    See Also
    --------
    scipy.integrate.quadrature
    scipy.integrate.fixed_quad
    numpy.polynomial.legendre.leggauss

    References
    ----------
    .. [AS] Milton Abramowitz and Irene A. Stegun, eds.
        Handbook of Mathematical Functions with Formulas,
        Graphs, and Mathematical Tables. New York: Dover, 1972.