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SciPy

This is documentation for an old release of SciPy (version 0.18.1). Read this page in the documentation of the latest stable release (version 1.15.1).

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 [R464],

jn(z)=π2zJn+1/2(z),

where Jn 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 [R465]. 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 [R466],

jn=jn1n+12jn.j0=j1

New in version 0.18.0.

References

[R464](1, 2) http://dlmf.nist.gov/10.47.E3
[R465](1, 2) http://dlmf.nist.gov/10.51.E1
[R466](1, 2) http://dlmf.nist.gov/10.51.E2