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.
- varray_like of float
Order of Bessel function
- zarray_like of complex
Argument at which to evaluate the derivative
Order of derivative. Default is first derivative.
The derivative is computed using the relation DLFM 10.29.5 .
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
NIST Digital Library of Mathematical Functions. https://dlmf.nist.gov/10.29.E5
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])