# scipy.special.spherical_jn¶

scipy.special.spherical_jn(n, z, derivative=False)[source]

Spherical Bessel function of the first kind or its derivative.

Defined as [1],

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

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. jn : ndarray

Notes

For real arguments greater than the order, the function is computed using the ascending recurrence [2]. 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 [3],

\begin{align}\begin{aligned}j_n'(z) = j_{n-1}(z) - \frac{n + 1}{z} j_n(z).\\j_0'(z) = -j_1(z)\end{aligned}\end{align}

New in version 0.18.0.

References

 [1] (1, 2) https://dlmf.nist.gov/10.47.E3
 [2] (1, 2) https://dlmf.nist.gov/10.51.E1
 [3] (1, 2) https://dlmf.nist.gov/10.51.E2

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