Module « scipy.special »

Fonction legendre - module scipy.special

Signature de la fonction legendre

def legendre(n, monic=False) 

Description

legendre.__doc__

Legendre polynomial.

    Defined to be the solution of

    .. math::
        \frac{d}{dx}\left[(1 - x^2)\frac{d}{dx}P_n(x)\right]
          + n(n + 1)P_n(x) = 0;

    :math:`P_n(x)` is a polynomial of degree :math:`n`.

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

    Returns
    -------
    P : orthopoly1d
        Legendre polynomial.

    Notes
    -----
    The polynomials :math:`P_n` are orthogonal over :math:`[-1, 1]`
    with weight function 1.

    Examples
    --------
    Generate the 3rd-order Legendre polynomial 1/2*(5x^3 + 0x^2 - 3x + 0):

    >>> from scipy.special import legendre
    >>> legendre(3)
    poly1d([ 2.5,  0. , -1.5,  0. ])