`scipy.special._basic:jvp`

source: build-install/usr/lib/python3.14/site-packages/scipy/special/_basic.py:818

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)

✗

(np.float64(0.7651976865579666), np.float64(-0.44005058574493355), np.float64(-0.3251471008130331))

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)

✗

array([-0.44 ,  0.325,  0.21 ])

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)

✗

array([-0.   , -0.558, -0.339])

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()

✗

<matplotlib.legend.Legend object at 0x7f3f684f4d70>

plt.show()

✓

Aliases

scipy.special.jvp