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:

Parameters:	v : array_like of float Order of Bessel function z : array_like of complex Argument at which to evaluate the derivative n : int Order of derivative. Default is first derivative.
Returns:	out : ndarray The results

v : array_like of float

Order of Bessel function

z : array_like of complex

Argument at which to evaluate the derivative

n : int

Order of derivative. Default is first derivative.

Returns:

out : ndarray

The results

Notes

The derivative is computed using the relation DLFM 10.29.5 [R531].

References

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

[R531]

(1, 2) NIST Digital Library of Mathematical Functions. http://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([-1849.0354+0.j    ,   -25.7735+0.j    ,    -0.0307+0.0875j])

Calculate for a single value at multiple orders:

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