scipy.special.kvp#

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

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/f77_src/special_functions/special_functions.html
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])