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# scipy.special.spherical_jn

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

  Spherical Bessel function of the first kind or its derivative.

  Defined as [R497],

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

  where \(J_n\) is the 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: | jn : ndarray

  Notes

  For real arguments greater than the order, the function is computed using the ascending recurrence [R498]. For small real or complex arguments, the definitional relation to the cylindrical Bessel function of the first kind is used.

  The derivative is computed using the relations [R499],

  \[ \begin{align}\begin{aligned}j_n' = j_{n-1} - \frac{n + 1}{2} j_n.\\j_0' = -j_1\end{aligned}\end{align} \]

  New in version 0.18.0.

  References

  [R497] | (1, 2) http://dlmf.nist.gov/10.47.E3

  [R498] | (1, 2) http://dlmf.nist.gov/10.51.E1

  [R499] | (1, 2) http://dlmf.nist.gov/10.51.E2