Module « scipy.special »

Fonction hermite - module scipy.special

Signature de la fonction hermite

def hermite(n, monic=False) 

Description

hermite.__doc__

Physicist's Hermite polynomial.

    Defined by

    .. math::

        H_n(x) = (-1)^ne^{x^2}\frac{d^n}{dx^n}e^{-x^2};

    :math:`H_n` 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
    -------
    H : orthopoly1d
        Hermite polynomial.

    Notes
    -----
    The polynomials :math:`H_n` are orthogonal over :math:`(-\infty,
    \infty)` with weight function :math:`e^{-x^2}`.

    Examples
    --------
    >>> from scipy import special
    >>> import matplotlib.pyplot as plt
    >>> import numpy as np

    >>> p_monic = special.hermite(3, monic=True)
    >>> p_monic
    poly1d([ 1. ,  0. , -1.5,  0. ])
    >>> p_monic(1)
    -0.49999999999999983
    >>> x = np.linspace(-3, 3, 400)
    >>> y = p_monic(x)
    >>> plt.plot(x, y)
    >>> plt.title("Monic Hermite polynomial of degree 3")
    >>> plt.xlabel("x")
    >>> plt.ylabel("H_3(x)")
    >>> plt.show()