`scipy.special._basic:yvp`

source: build-install/usr/lib/python3.14/site-packages/scipy/special/_basic.py:896

Signature

def yvp(v, z, n = 1)

Summary

Compute derivatives of Bessel functions of the second kind.

Extended Summary

Compute the nth derivative of the Bessel function Yv with respect to z.

Parameters

v : array_like of float: Order of Bessel function
z : complex: Argument at which to evaluate the derivative
n : int, default 1: Order of derivative. For 0 returns the BEssel function yv

Returns

: scalar or ndarray: nth derivative of the Bessel function.

Notes

The derivative is computed using the relation DLFM 10.6.7 ^[2].

Examples

Compute the Bessel function of the second kind of order 0 and its first two derivatives at 1.

from scipy.special import yvp

✓

yvp(0, 1, 0), yvp(0, 1, 1), yvp(0, 1, 2)

✗

(np.float64(0.088256964215677), np.float64(0.7812128213002889), np.float64(-0.8694697855159659))

Compute the first derivative of the Bessel function of the second kind for several orders at 1 by providing an array for `v`.

yvp([0, 1, 2], 1, 1)

✗

array([0.78121, 0.86947, 2.52015])

Compute the first derivative of the Bessel function of the second kind of order 0 at several points by providing an array for `z`.

import numpy as np
points = np.array([0.5, 1.5, 3.])

✓

yvp(0, points, 1)

✗

array([ 1.47147,  0.41231, -0.32467])

Plot the Bessel function of the second kind of order 1 and its first three derivatives.

import matplotlib.pyplot as plt
x = np.linspace(0, 5, 1000)
x[0] += 1e-15
fig, ax = plt.subplots()

✓

ax.plot(x, yvp(1, x, 0), label=r"$Y_1$")
ax.plot(x, yvp(1, x, 1), label=r"$Y_1'$")
ax.plot(x, yvp(1, x, 2), label=r"$Y_1''$")
ax.plot(x, yvp(1, x, 3), label=r"$Y_1'''$")
ax.set_ylim(-10, 10)
plt.legend()

✗

<matplotlib.legend.Legend object at 0x7f3f590a3770>

plt.show()

✓

Aliases

scipy.special.yvp