scipy.special.kvp

scipy.special.kvp(v, z, n=1)

Compute nth derivative of real-order modified Bessel function Kv(z)

Kv(z) is the modified Bessel function of the second kind. Derivative is calculated with respect to z.

Parameters

varray_like of float

Order of Bessel function

zarray_like of complex

Argument at which to evaluate the derivative

nint

Order of derivative. Default is first derivative.

Returns

outndarray

The results

Notes

The derivative is computed using the relation DLFM 10.29.5 [2].

References

1

Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996, chapter 6. https://people.sc.fsu.edu/~jburkardt/f_src/special_functions/special_functions.html

2(1,2)

NIST Digital Library of Mathematical Functions. https://dlmf.nist.gov/10.29.E5

Examples

Calculate multiple values at order 5:

>>> from scipy.special import kvp
>>> kvp(5, (1, 2, 3+5j))
array([-1.84903536e+03+0.j        , -2.57735387e+01+0.j        ,
       -3.06627741e-02+0.08750845j])

Calculate for a single value at multiple orders:

>>> kvp((4, 4.5, 5), 1)
array([ -184.0309,  -568.9585, -1849.0354])