# 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],

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

where $$K_n$$ 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. 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],

$k_n' = -k_{n-1} - \frac{n + 1}{2} k_n.$$k_0' = -k_1$

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

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