`scipy.special._basic:ynp_zeros`

source: /scipy/special/_basic.py :505

Signature

def ynp_zeros ( n , nt )

Summary

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

Extended Summary

Compute nt zeros of the functions $Y_{n}^{'} (x)$ on the interval $(0, \infty)$ . 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.

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)

✗

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()

✓

Aliases

scipy.special.ynp_zeros