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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_in

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

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

Defined as [R462],

in(z)=π2zIn+1/2(z),

where In 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 [R463],

in=in1n+12in.i1=i0

New in version 0.18.0.

References

[R462](1, 2) http://dlmf.nist.gov/10.47.E7
[R463](1, 2) http://dlmf.nist.gov/10.51.E5