`scipy.special._basic:jnp_zeros`

source: build-install/usr/lib/python3.14/site-packages/scipy/special/_basic.py:385

Signature

def jnp_zeros(n, nt)

Summary

Compute zeros of integer-order Bessel function derivatives Jn'.

Extended Summary

Compute nt zeros of the 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 $n > 1$ .

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 roots of :math:`J_2'`.

from scipy.special import jnp_zeros

✓

jnp_zeros(2, 4)

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array([ 3.054,  6.706,  9.969, 13.17 ])

As `jnp_zeros` yields the roots of :math:`J_n'`, it can be used to compute the locations of the peaks of :math:`J_n`. Plot :math:`J_2`, :math:`J_2'` and the locations of the roots of :math:`J_2'`.

import numpy as np
import matplotlib.pyplot as plt
from scipy.special import jn, jnp_zeros, jvp
j2_roots = jnp_zeros(2, 4)
xmax = 15
x = np.linspace(0, xmax, 500)
fig, ax = plt.subplots()

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ax.plot(x, jn(2, x), label=r'$J_2$')
ax.plot(x, jvp(2, x, 1), label=r"$J_2'$")
ax.hlines(0, 0, xmax, color='k')
ax.scatter(j2_roots, np.zeros((4, )), s=30, c='r',
           label=r"Roots of $J_2'$", zorder=5)
ax.set_ylim(-0.4, 0.8)
ax.set_xlim(0, xmax)
plt.legend()

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<matplotlib.legend.Legend object at 0x7f3f685496a0>

plt.show()

✓

Aliases

scipy.special.jnp_zeros