Module « scipy.special »

Fonction roots_jacobi - module scipy.special

Signature de la fonction roots_jacobi

def roots_jacobi(n, alpha, beta, mu=False) 

Description

roots_jacobi.__doc__

Gauss-Jacobi quadrature.

    Compute the sample points and weights for Gauss-Jacobi
    quadrature. The sample points are the roots of the nth degree
    Jacobi polynomial, :math:`P^{\alpha, \beta}_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)^{\alpha} (1 +
    x)^{\beta}`. See 22.2.1 in [AS]_ for details.

    Parameters
    ----------
    n : int
        quadrature order
    alpha : float
        alpha must be > -1
    beta : float
        beta must be > -1
    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.