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SciPy

This is documentation for an old release of SciPy (version 0.19.0). Read this page in the documentation of the latest stable release (version 1.15.1).

scipy.special.spherical_yn

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

Spherical Bessel function of the second kind or its derivative.

Defined as [R529],

yn(z)=π2zYn+1/2(z),

where Yn is the Bessel function of the second 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:

yn : ndarray

Notes

For real arguments, the function is computed using the ascending recurrence [R530]. For complex arguments, the definitional relation to the cylindrical Bessel function of the second kind is used.

The derivative is computed using the relations [R531],

yn=yn1n+12yn.y0=y1

New in version 0.18.0.

References

[R529](1, 2) http://dlmf.nist.gov/10.47.E4
[R530](1, 2) http://dlmf.nist.gov/10.51.E1
[R531](1, 2) http://dlmf.nist.gov/10.51.E2