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Module « scipy.special »

Fonction ynp_zeros - module scipy.special

Signature de la fonction ynp_zeros

def ynp_zeros(n, nt) 

Description

help(scipy.special.ynp_zeros)

Compute zeros of integer-order Bessel function derivatives Yn'(x).

Compute `nt` zeros of the functions :math:`Y_n'(x)` on the
interval :math:`(0, \infty)`. The zeros are returned in ascending
order.

Parameters
----------
n : int
    Order of Bessel function
nt : int
    Number of zeros to return

Returns
-------
ndarray
    First `nt` zeros of the Bessel derivative function.


See Also
--------
yvp

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

Examples
--------
Compute the first four roots of the first derivative of the
Bessel function of second kind for order 0 :math:`Y_0'`.

>>> from scipy.special import ynp_zeros
>>> ynp_zeros(0, 4)
array([ 2.19714133,  5.42968104,  8.59600587, 11.74915483])

Plot :math:`Y_0`, :math:`Y_0'` and confirm visually that the roots of
:math:`Y_0'` are located at local extrema of :math:`Y_0`.

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.special import yn, ynp_zeros, yvp
>>> zeros = ynp_zeros(0, 4)
>>> xmax = 13
>>> x = np.linspace(0, xmax, 500)
>>> fig, ax = plt.subplots()
>>> ax.plot(x, yn(0, x), label=r'$Y_0$')
>>> ax.plot(x, yvp(0, x, 1), label=r"$Y_0'$")
>>> ax.scatter(zeros, np.zeros((4, )), s=30, c='r',
...            label=r"Roots of $Y_0'$", zorder=5)
>>> for root in zeros:
...     y0_extremum =  yn(0, root)
...     lower = min(0, y0_extremum)
...     upper = max(0, y0_extremum)
...     ax.vlines(root, lower, upper, color='r')
>>> ax.hlines(0, 0, xmax, color='k')
>>> ax.set_ylim(-0.6, 0.6)
>>> ax.set_xlim(0, xmax)
>>> plt.legend()
>>> plt.show()

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