scipy.special.h2vp

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.

See also

hankel2

Notes

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

References

1

Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996, chapter 5. https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html

2

NIST Digital Library of Mathematical Functions. https://dlmf.nist.gov/10.6.E7

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])