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Module « scipy.special »

Fonction y1 - module scipy.special

Signature de la fonction y1

def y1(*args, **kwargs) 

Description

help(scipy.special.y1)

y1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    y1(x, out=None)

    Bessel function of the second kind of order 1.

    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 1 at `x`.

    See Also
    --------
    j1: Bessel function of the first kind of order 1
    yn: Bessel function of the second kind
    yv: Bessel function of the second kind

    Notes
    -----
    The domain is divided into the intervals [0, 8] and (8, infinity). In the
    first interval a 25 term Chebyshev expansion is used, and computing
    :math:`J_1` (the Bessel function of the first kind) is required. In the
    second, the asymptotic trigonometric representation is employed using two
    rational functions of degree 5/5.

    This function is a wrapper for the Cephes [1]_ routine `y1`.

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

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

    >>> from scipy.special import y1
    >>> y1(1.)
    -0.7812128213002888

    Calculate at several points:

    >>> import numpy as np
    >>> y1(np.array([0.5, 2., 3.]))
    array([-1.47147239, -0.10703243,  0.32467442])

    Plot the function from 0 to 10.

    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots()
    >>> x = np.linspace(0., 10., 1000)
    >>> y = y1(x)
    >>> ax.plot(x, y)
    >>> plt.show()
    

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