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 [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
- nint, array_like
Order of the Bessel function (n >= 0).
- zcomplex or float, array_like
Argument of the Bessel function.
- derivativebool, optional
If True, the value of the derivative (rather than the function itself) is returned.
- Returns
- ynndarray
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