Loading [MathJax]/jax/output/HTML-CSS/jax.js
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_kn

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

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

Defined as [R467],

kn(z)=π2zKn+1/2(z),

where Kn is the modified 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:

kn : ndarray

Notes

The function is computed using its definitional relation to the modified cylindrical Bessel function of the second kind.

The derivative is computed using the relations [R468],

kn=kn1n+12kn.k0=k1

New in version 0.18.0.

References

[R467](1, 2) http://dlmf.nist.gov/10.47.E9
[R468](1, 2) http://dlmf.nist.gov/10.51.E5