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Module « scipy.special »

Fonction j0 - module scipy.special

Signature de la fonction j0

def j0(*args, **kwargs) 

Description

help(scipy.special.j0)

j0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    j0(x, out=None)

    Bessel function of the first kind of order 0.

    Parameters
    ----------
    x : array_like
        Argument (float).
    out : ndarray, optional
        Optional output array for the function values

    Returns
    -------
    J : scalar or ndarray
        Value of the Bessel function of the first kind of order 0 at `x`.

    See Also
    --------
    jv : Bessel function of real order and complex argument.
    spherical_jn : spherical Bessel functions.

    Notes
    -----
    The domain is divided into the intervals [0, 5] and (5, infinity). In the
    first interval the following rational approximation is used:

    .. math::

        J_0(x) \approx (w - r_1^2)(w - r_2^2) \frac{P_3(w)}{Q_8(w)},

    where :math:`w = x^2` and :math:`r_1`, :math:`r_2` are the zeros of
    :math:`J_0`, and :math:`P_3` and :math:`Q_8` are polynomials of degrees 3
    and 8, respectively.

    In the second interval, the Hankel asymptotic expansion is employed with
    two rational functions of degree 6/6 and 7/7.

    This function is a wrapper for the Cephes [1]_ routine `j0`.
    It should not be confused with the spherical Bessel functions (see
    `spherical_jn`).

    References
    ----------
    .. [1] Cephes Mathematical Functions Library,
           http://www.netlib.org/cephes/

    Examples
    --------
    Calculate the function at one point:

    >>> from scipy.special import j0
    >>> j0(1.)
    0.7651976865579665

    Calculate the function at several points:

    >>> import numpy as np
    >>> j0(np.array([-2., 0., 4.]))
    array([ 0.22389078,  1.        , -0.39714981])

    Plot the function from -20 to 20.

    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots()
    >>> x = np.linspace(-20., 20., 1000)
    >>> y = j0(x)
    >>> ax.plot(x, y)
    >>> plt.show()
    

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