# 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.

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  routine k0.

References



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

Examples

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()