scipy.special.

h2vp#

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

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

Parameters:
varray_like

Order of Hankel function

zarray_like

Argument at which to evaluate the derivative. Can be real orcomplex.

nint, default 1

Order of derivative. For 0 returns the Hankel functionhankel2 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 SpecialFunctions”, 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 andits first two derivatives at 1.

>>>fromscipy.specialimporth2vp>>>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 kindfor several orders at 1 by providing an array forv.

>>>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 kindof order 0 at several points by providing an array forz.

>>>importnumpyasnp>>>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])
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