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Module « scipy.special »

Fonction yvp - module scipy.special

Signature de la fonction yvp

def yvp(v, z, n=1) 

Description

help(scipy.special.yvp)

Compute derivatives of Bessel functions of the second kind.

Compute the nth derivative of the Bessel function `Yv` with
respect to `z`.

Parameters
----------
v : array_like of float
    Order of Bessel function
z : complex
    Argument at which to evaluate the derivative
n : int, default 1
    Order of derivative. For 0 returns the BEssel function `yv`

Returns
-------
scalar or ndarray
    nth derivative of the Bessel function.

See Also
--------
yv : Bessel functions of the second kind

Notes
-----
The derivative is computed using the relation DLFM 10.6.7 [2]_.

References
----------
.. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special
       Functions", John Wiley and Sons, 1996, chapter 5.
       https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html

.. [2] NIST Digital Library of Mathematical Functions.
       https://dlmf.nist.gov/10.6.E7

Examples
--------
Compute the Bessel function of the second kind of order 0 and
its first two derivatives at 1.

>>> from scipy.special import yvp
>>> yvp(0, 1, 0), yvp(0, 1, 1), yvp(0, 1, 2)
(0.088256964215677, 0.7812128213002889, -0.8694697855159659)

Compute the first derivative of the Bessel function of the second
kind for several orders at 1 by providing an array for `v`.

>>> yvp([0, 1, 2], 1, 1)
array([0.78121282, 0.86946979, 2.52015239])

Compute the first derivative of the Bessel function of the
second kind of order 0 at several points by providing an array for `z`.

>>> import numpy as np
>>> points = np.array([0.5, 1.5, 3.])
>>> yvp(0, points, 1)
array([ 1.47147239,  0.41230863, -0.32467442])

Plot the Bessel function of the second kind of order 1 and its
first three derivatives.

>>> import matplotlib.pyplot as plt
>>> x = np.linspace(0, 5, 1000)
>>> x[0] += 1e-15
>>> fig, ax = plt.subplots()
>>> ax.plot(x, yvp(1, x, 0), label=r"$Y_1$")
>>> ax.plot(x, yvp(1, x, 1), label=r"$Y_1'$")
>>> ax.plot(x, yvp(1, x, 2), label=r"$Y_1''$")
>>> ax.plot(x, yvp(1, x, 3), label=r"$Y_1'''$")
>>> ax.set_ylim(-10, 10)
>>> plt.legend()
>>> plt.show()

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