h2vp — SciPy v1.15.2 Manual (original) (raw)

scipy.special.

scipy.special.h2vp(v, z, n=1)[source]#

Compute derivatives of Hankel function H2v(z) with respect to z.

Parameters:

varray_like

Order of Hankel function

zarray_like

Argument at which to evaluate the derivative. Can be real or complex.

nint, default 1

Order of derivative. For 0 returns the Hankel function h2v 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].

References

Examples

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

from scipy.special import h2vp h2vp(0, 1, 0), h2vp(0, 1, 1), h2vp(0, 1, 2) ((0.7651976865579664-0.088256964215677j), (-0.44005058574493355-0.7812128213002889j), (-0.3251471008130329+0.8694697855159659j))

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

h2vp([0, 1, 2], 1, 1) array([-0.44005059-0.78121282j, 0.3251471 -0.86946979j, 0.21024362-2.52015239j])

Compute the first derivative of the Hankel 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.]) h2vp(0, points, 1) array([-0.24226846-1.47147239j, -0.55793651-0.41230863j, -0.33905896+0.32467442j])