`scipy.special._basic:jn_zeros`

source: build-install/usr/lib/python3.14/site-packages/scipy/special/_basic.py:322

Signature

def jn_zeros(n, nt)

Summary

Compute zeros of integer-order Bessel functions Jn.

Extended Summary

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

Parameters

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

Returns

: ndarray: First nt zeros of the Bessel function.

Examples

Compute the first four positive roots of :math:`J_3`.

from scipy.special import jn_zeros

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jn_zeros(3, 4)

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array([ 6.38 ,  9.761, 13.015, 16.223])

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()

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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()

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<matplotlib.legend.Legend object at 0x7f3f68aef770>

plt.show()

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Aliases

scipy.special.jn_zeros