# scipy.special.spherical_yn

scipy.special.spherical_yn(n, z, derivative=False)

  Spherical Bessel function of the second kind or its derivative.

  Defined as [1],

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

  where \(Y_n\) is the 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
    yn ndarray

  Notes

  For real arguments, the function is computed using the ascending recurrence [2]. For complex arguments, the definitional relation to the cylindrical Bessel function of the second kind is used.

  The derivative is computed using the relations [3],

  \[ \begin{align}\begin{aligned}y_n' = y_{n-1} - \frac{n + 1}{z} y_n.\\y_0' = -y_1\end{aligned}\end{align} \]

  New in version 0.18.0.

  References

  1

    https://dlmf.nist.gov/10.47.E4

  2

    https://dlmf.nist.gov/10.51.E1

  3

    https://dlmf.nist.gov/10.51.E2

scipy.special.spherical_jn scipy.special.spherical_in