scipy.special.k0

scipy.special.k0(x, out=None) = <ufunc 'k0'>

Modified Bessel function of the second kind of order 0, \(K_0\).

This function is also sometimes referred to as the modified Bessel function of the third kind of order 0.

Parameters:

xarray_like

Argument (float).

outndarray, optional

Optional output array for the function values

Returns:

Kscalar or ndarray

Value of the modified Bessel function \(K_0\) at x.

See also

kv

Modified Bessel function of the second kind of any order

k0e

Exponentially scaled modified Bessel function of the second kind

Notes

The range is partitioned into the two intervals [0, 2] and (2, infinity). Chebyshev polynomial expansions are employed in each interval.

This function is a wrapper for the Cephes [1] routine k0.

References

[1]

Cephes Mathematical Functions Library, http://www.netlib.org/cephes/

Examples

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Calculate the function at one point:

>>> from scipy.special import k0
>>> k0(1.)
0.42102443824070823

Calculate the function at several points:

>>> import numpy as np
>>> k0(np.array([0.5, 2., 3.]))
array([0.92441907, 0.11389387, 0.0347395 ])

Plot the function from 0 to 10.

>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> x = np.linspace(0., 10., 1000)
>>> y = k0(x)
>>> ax.plot(x, y)
>>> plt.show()

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