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
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])