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# scipy.special.spherical_kn

`scipy.special.``spherical_kn`(n, z, derivative=False)

  Modified spherical Bessel function of the second kind or its derivative.

  Defined as [R527],

  \[k_n(z) = \sqrt{\frac{\pi}{2z}} K_{n + 1/2}(z),\]

  where \(K_n\) is the modified Bessel function of the second kind.

  Parameters: | n : int, array_like Order of the Bessel function (n >= 0). z : complex or float, array_like Argument of the Bessel function. derivative : bool, optional If True, the value of the derivative (rather than the function itself) is returned.
  Returns: | kn : ndarray

  Notes

  The function is computed using its definitional relation to the modified cylindrical Bessel function of the second kind.

  The derivative is computed using the relations [R528],

  \[ \begin{align}\begin{aligned}k_n' = -k_{n-1} - \frac{n + 1}{2} k_n.\\k_0' = -k_1\end{aligned}\end{align} \]

  New in version 0.18.0.

  References

  [R527] | (1, 2) http://dlmf.nist.gov/10.47.E9

  [R528] | (1, 2) http://dlmf.nist.gov/10.51.E5