# 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 [1],

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

  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 [2],

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

  New in version 0.18.0.

  References

  1

    https://dlmf.nist.gov/10.47.E9

  2

    https://dlmf.nist.gov/10.51.E5

scipy.special.spherical_in scipy.special.riccati_jn