- scipy.special.h1vp(v, z, n=1)#
Compute derivatives of Hankel function H1v(z) with respect to z.
Order of Hankel function
Argument at which to evaluate the derivative. Can be real or complex.
- nint, default 1
Order of derivative. For 0 returns the Hankel function h1v itself.
- scalar or ndarray
Values of the derivative of the Hankel function.
The derivative is computed using the relation DLFM 10.6.7 .
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
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) ((0.7651976865579664+0.088256964215677j), (-0.44005058574493355+0.7812128213002889j), (-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([-0.44005059+0.78121282j, 0.3251471 +0.86946979j, 0.21024362+2.52015239j])
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([-0.24226846+1.47147239j, -0.55793651+0.41230863j, -0.33905896-0.32467442j])