scipy.special.spherical_in¶
-
scipy.special.spherical_in(n, z, derivative=False)[source]¶ Modified spherical Bessel function of the first kind or its derivative.
Defined as [1],
\[i_n(z) = \sqrt{\frac{\pi}{2z}} I_{n + 1/2}(z),\]where \(I_n\) is the modified Bessel function of the first 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
- inndarray
Notes
The function is computed using its definitional relation to the modified cylindrical Bessel function of the first kind.
The derivative is computed using the relations [2],
\[ \begin{align}\begin{aligned}i_n' = i_{n-1} - \frac{n + 1}{z} i_n.\\i_1' = i_0\end{aligned}\end{align} \]New in version 0.18.0.
References