scipy.special.k1#
- scipy.special.k1(x, out=None) = <ufunc 'k1'>#
Modified Bessel function of the second kind of order 1, \(K_1(x)\).
- 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 of order 1 at x.
See also
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
k1
.References
[1]Cephes Mathematical Functions Library, http://www.netlib.org/cephes/
Examples
Calculate the function at one point:
>>> from scipy.special import k1 >>> k1(1.) 0.6019072301972346
Calculate the function at several points:
>>> import numpy as np >>> k1(np.array([0.5, 2., 3.])) array([1.65644112, 0.13986588, 0.04015643])
Plot the function from 0 to 10.
>>> import matplotlib.pyplot as plt >>> fig, ax = plt.subplots() >>> x = np.linspace(0., 10., 1000) >>> y = k1(x) >>> ax.plot(x, y) >>> plt.show()