Module « scipy.special »

Fonction genlaguerre - module scipy.special

Signature de la fonction genlaguerre

def genlaguerre(n, alpha, monic=False) 

Description

genlaguerre.__doc__

Generalized (associated) Laguerre polynomial.

    Defined to be the solution of

    .. math::
        x\frac{d^2}{dx^2}L_n^{(\alpha)}
          + (\alpha + 1 - x)\frac{d}{dx}L_n^{(\alpha)}
          + nL_n^{(\alpha)} = 0,

    where :math:`\alpha > -1`; :math:`L_n^{(\alpha)}` is a polynomial
    of degree :math:`n`.

    Parameters
    ----------
    n : int
        Degree of the polynomial.
    alpha : float
        Parameter, must be greater than -1.
    monic : bool, optional
        If `True`, scale the leading coefficient to be 1. Default is
        `False`.

    Returns
    -------
    L : orthopoly1d
        Generalized Laguerre polynomial.

    Notes
    -----
    For fixed :math:`\alpha`, the polynomials :math:`L_n^{(\alpha)}`
    are orthogonal over :math:`[0, \infty)` with weight function
    :math:`e^{-x}x^\alpha`.

    The Laguerre polynomials are the special case where :math:`\alpha
    = 0`.

    See Also
    --------
    laguerre : Laguerre polynomial.