# 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
    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 [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

    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])

scipy.special.yvp scipy.special.ivp