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Module « scipy.special »

Fonction yn - module scipy.special

Signature de la fonction yn

def yn(*args, **kwargs) 

Description

help(scipy.special.yn)

yn(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

yn(n, x, out=None)

Bessel function of the second kind of integer order and real argument.

Parameters
----------
n : array_like
    Order (integer).
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, :math:`Y_n(x)`.

See Also
--------
yv : For real order and real or complex argument.
y0: faster implementation of this function for order 0
y1: faster implementation of this function for order 1

Notes
-----
Wrapper for the Cephes [1]_ routine `yn`.

The function is evaluated by forward recurrence on `n`, starting with
values computed by the Cephes routines `y0` and `y1`. If ``n = 0`` or 1,
the routine for `y0` or `y1` is called directly.

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

Examples
--------
Evaluate the function of order 0 at one point.

>>> from scipy.special import yn
>>> yn(0, 1.)
0.08825696421567697

Evaluate the function at one point for different orders.

>>> yn(0, 1.), yn(1, 1.), yn(2, 1.)
(0.08825696421567697, -0.7812128213002888, -1.6506826068162546)

The evaluation for different orders can be carried out in one call by
providing a list or NumPy array as argument for the `v` parameter:

>>> yn([0, 1, 2], 1.)
array([ 0.08825696, -0.78121282, -1.65068261])

Evaluate the function at several points for order 0 by providing an
array for `z`.

>>> import numpy as np
>>> points = np.array([0.5, 3., 8.])
>>> yn(0, points)
array([-0.44451873,  0.37685001,  0.22352149])

If `z` is an array, the order parameter `v` must be broadcastable to
the correct shape if different orders shall be computed in one call.
To calculate the orders 0 and 1 for an 1D array:

>>> orders = np.array([[0], [1]])
>>> orders.shape
(2, 1)

>>> yn(orders, points)
array([[-0.44451873,  0.37685001,  0.22352149],
       [-1.47147239,  0.32467442, -0.15806046]])

Plot the functions of order 0 to 3 from 0 to 10.

>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> x = np.linspace(0., 10., 1000)
>>> for i in range(4):
...     ax.plot(x, yn(i, x), label=f'$Y_{i!r}$')
>>> ax.set_ylim(-3, 1)
>>> ax.legend()
>>> plt.show()

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