# 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

1

https://dlmf.nist.gov/10.47.E7

2

https://dlmf.nist.gov/10.51.E5

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