`scipy.special._basic:yvp`

source: /scipy/special/_basic.py :895

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)

✗

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)

✗

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)

✗

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()

✗

plt.show()

✓

Aliases

scipy.special.yvp