scipy.special.k0 — SciPy v1.15.2 Manual (original) (raw)
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
Modified Bessel function of the second kind of any order
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
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()
