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# scipy.special.spherical_in

`scipy.special.``spherical_in`(n, z, derivative=False)

  Modified spherical Bessel function of the first kind or its derivative.

  Defined as [R495],

  \[i_n(z) = \sqrt{\frac{\pi}{2z}} I_{n + 1/2}(z),\]

  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 [R496],

  \[ \begin{align}\begin{aligned}i_n' = i_{n-1} - \frac{n + 1}{2} i_n.\\i_1' = i_0\end{aligned}\end{align} \]

  New in version 0.18.0.

  References

  [R495] | (1, 2) http://dlmf.nist.gov/10.47.E7

  [R496] | (1, 2) http://dlmf.nist.gov/10.51.E5