# scipy.special.spherical_yn¶

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

Spherical Bessel function of the second kind or its derivative.

Defined as [R529],

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

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. yn : ndarray

Notes

For real arguments, the function is computed using the ascending recurrence [R530]. For complex arguments, the definitional relation to the cylindrical Bessel function of the second kind is used.

The derivative is computed using the relations [R531],

\begin{align}\begin{aligned}y_n' = y_{n-1} - \frac{n + 1}{2} y_n.\\y_0' = -y_1\end{aligned}\end{align}

New in version 0.18.0.

References

 [R529] (1, 2) http://dlmf.nist.gov/10.47.E4
 [R530] (1, 2) http://dlmf.nist.gov/10.51.E1
 [R531] (1, 2) http://dlmf.nist.gov/10.51.E2