# 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: 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. 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 [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

 [1] (1, 2) http://dlmf.nist.gov/10.47.E7
 [2] (1, 2) http://dlmf.nist.gov/10.51.E5

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