`scipy.special._basic:h1vp`

source: build-install/usr/lib/python3.14/site-packages/scipy/special/_basic.py:1140

Signature

def h1vp(v, z, n = 1)

Summary

Compute derivatives of Hankel function H1v(z) with respect to z.

Parameters

v : array_like: Order of Hankel function
z : array_like: Argument at which to evaluate the derivative. Can be real or complex.
n : int, default 1: Order of derivative. For 0 returns the Hankel function hankel1 itself.

Returns

: scalar or ndarray: Values of the derivative of the Hankel function.

Notes

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

Examples

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

from scipy.special import h1vp

✓

h1vp(0, 1, 0), h1vp(0, 1, 1), h1vp(0, 1, 2)

✗

(np.complex128(0.7651976865579664+0.088256964215677j), np.complex128(-0.44005058574493355+0.7812128213002889j), np.complex128(-0.3251471008130329-0.8694697855159659j))

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

h1vp([0, 1, 2], 1, 1)

✗

array([-0.44 +0.781j,  0.325+0.869j,  0.21 +2.52j ])

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

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

✓

h1vp(0, points, 1)

✗

array([-0.242+1.471j, -0.558+0.412j, -0.339-0.325j])

Aliases

scipy.special.h1vp