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Module « scipy.special »

Fonction y0 - module scipy.special

Signature de la fonction y0

def y0(*args, **kwargs) 

Description

help(scipy.special.y0)

y0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    y0(x, out=None)

    Bessel function of the second kind of order 0.

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

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

    See Also
    --------
    j0: Bessel function of the first kind of order 0
    yv: Bessel function of the first kind

    Notes
    -----
    The domain is divided into the intervals [0, 5] and (5, infinity). In the
    first interval a rational approximation :math:`R(x)` is employed to
    compute,

    .. math::

        Y_0(x) = R(x) + \frac{2 \log(x) J_0(x)}{\pi},

    where :math:`J_0` is the Bessel function of the first kind of order 0.

    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 `y0`.

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

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

    >>> from scipy.special import y0
    >>> y0(1.)
    0.08825696421567697

    Calculate at several points:

    >>> import numpy as np
    >>> y0(np.array([0.5, 2., 3.]))
    array([-0.44451873,  0.51037567,  0.37685001])

    Plot the function from 0 to 10.

    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots()
    >>> x = np.linspace(0., 10., 1000)
    >>> y = y0(x)
    >>> ax.plot(x, y)
    >>> plt.show()
    

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