Module « scipy.special »

Fonction roots_gegenbauer - module scipy.special

Signature de la fonction roots_gegenbauer

def roots_gegenbauer(n, alpha, mu=False) 

Description

roots_gegenbauer.__doc__

Gauss-Gegenbauer quadrature.

    Compute the sample points and weights for Gauss-Gegenbauer
    quadrature. The sample points are the roots of the nth degree
    Gegenbauer polynomial, :math:`C^{\alpha}_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 - x^2)^{\alpha - 1/2}`. See
    22.2.3 in [AS]_ for more details.

    Parameters
    ----------
    n : int
        quadrature order
    alpha : float
        alpha must be > -0.5
    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

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