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Module « scipy.special »

Fonction h1vp - module scipy.special

Signature de la fonction h1vp

def h1vp(v, z, n=1) 

Description

help(scipy.special.h1vp)

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 `h1v` itself.

Returns
-------
scalar or ndarray
    Values of the derivative of the Hankel function.

See Also
--------
hankel1

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 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])

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