`scipy.special._basic:jvp`

source: /scipy/special/_basic.py :817

Signature

def jvp ( v , z , n = 1 )

Summary

Compute derivatives of Bessel functions of the first kind.

Extended Summary

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

Parameters

v : array_like or float: Order of Bessel function
z : complex: Argument at which to evaluate the derivative; can be real or complex.
n : int, default 1: Order of derivative. For 0 returns the Bessel function jv itself.

Returns

: scalar or ndarray: Values of the 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 first kind of order 0 and its first two derivatives at 1.

from scipy.special import jvp

✓

jvp(0, 1, 0), jvp(0, 1, 1), jvp(0, 1, 2)

✗

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

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

✗

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

import numpy as np
points = np.array([0., 1.5, 3.])

✓

jvp(0, points, 1)

✗

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

import matplotlib.pyplot as plt
x = np.linspace(-10, 10, 1000)
fig, ax = plt.subplots()

✓

ax.plot(x, jvp(1, x, 0), label=r"$J_1$")
ax.plot(x, jvp(1, x, 1), label=r"$J_1'$")
ax.plot(x, jvp(1, x, 2), label=r"$J_1''$")
ax.plot(x, jvp(1, x, 3), label=r"$J_1'''$")
plt.legend()

✗

plt.show()

✓

Aliases

scipy.special.jvp