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 [R462],
\[i_n(z) = \sqrt{\frac{\pi}{2z}} I_{n + 1/2}(z),\]where \(I_n\) is the modified Bessel function of the first kind.
Parameters: 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: in : ndarray
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 [R463],
\[i_n' = i_{n-1} - \frac{n + 1}{2} i_n.\]\[i_1' = i_0\]New in version 0.18.0.
References
[R462] (1, 2) http://dlmf.nist.gov/10.47.E7 [R463] (1, 2) http://dlmf.nist.gov/10.51.E5