Module « scipy.special »

Fonction roots_genlaguerre - module scipy.special

Signature de la fonction roots_genlaguerre

def roots_genlaguerre(n, alpha, mu=False) 

Description

roots_genlaguerre.__doc__

Gauss-generalized Laguerre quadrature.

    Compute the sample points and weights for Gauss-generalized
    Laguerre quadrature. The sample points are the roots of the nth
    degree generalized Laguerre polynomial, :math:`L^{\alpha}_n(x)`.
    These sample points and weights correctly integrate polynomials of
    degree :math:`2n - 1` or less over the interval :math:`[0,
    \infty]` with weight function :math:`w(x) = x^{\alpha}
    e^{-x}`. See 22.3.9 in [AS]_ for details.

    Parameters
    ----------
    n : int
        quadrature order
    alpha : float
        alpha 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.