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Module « scipy.special »

Fonction jn_zeros - module scipy.special

Signature de la fonction jn_zeros

def jn_zeros(n, nt) 

Description

help(scipy.special.jn_zeros)

Compute zeros of integer-order Bessel functions Jn.

Compute `nt` zeros of the Bessel functions :math:`J_n(x)` on the
interval :math:`(0, \infty)`. The zeros are returned in ascending
order. Note that this interval excludes the zero at :math:`x = 0`
that exists for :math:`n > 0`.

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

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

See Also
--------
jv: Real-order Bessel functions of the first kind
jnp_zeros: Zeros of :math:`Jn'`

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 positive roots of :math:`J_3`.

>>> from scipy.special import jn_zeros
>>> jn_zeros(3, 4)
array([ 6.3801619 ,  9.76102313, 13.01520072, 16.22346616])

Plot :math:`J_3` and its first four positive roots. Note
that the root located at 0 is not returned by `jn_zeros`.

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.special import jn, jn_zeros
>>> j3_roots = jn_zeros(3, 4)
>>> xmax = 18
>>> xmin = -1
>>> x = np.linspace(xmin, xmax, 500)
>>> fig, ax = plt.subplots()
>>> ax.plot(x, jn(3, x), label=r'$J_3$')
>>> ax.scatter(j3_roots, np.zeros((4, )), s=30, c='r',
...            label=r"$J_3$_Zeros", zorder=5)
>>> ax.scatter(0, 0, s=30, c='k',
...            label=r"Root at 0", zorder=5)
>>> ax.hlines(0, 0, xmax, color='k')
>>> ax.set_xlim(xmin, xmax)
>>> plt.legend()
>>> plt.show()

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