scipy.special.kn#
- scipy.special.kn(n, x, out=None) = <ufunc 'kn'>#
Modified Bessel function of the second kind of integer order n
Returns the modified Bessel function of the second kind for integer order n at real z.
These are also sometimes called functions of the third kind, Basset functions, or Macdonald functions.
- Parameters:
- narray_like of int
Order of Bessel functions (floats will truncate with a warning)
- xarray_like of float
Argument at which to evaluate the Bessel functions
- outndarray, optional
Optional output array for the function results.
- Returns:
- scalar or ndarray
Value of the Modified Bessel function of the second kind, \(K_n(x)\).
See also
Notes
Wrapper for AMOS [1] routine zbesk. For a discussion of the algorithm used, see [2] and the references therein.
References
[1]Donald E. Amos, “AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order”, http://netlib.org/amos/
[2]Donald E. Amos, “Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order”, ACM TOMS Vol. 12 Issue 3, Sept. 1986, p. 265
Examples
Plot the function of several orders for real input:
>>> import numpy as np >>> from scipy.special import kn >>> import matplotlib.pyplot as plt >>> x = np.linspace(0, 5, 1000) >>> for N in range(6): ... plt.plot(x, kn(N, x), label='$K_{}(x)$'.format(N)) >>> plt.ylim(0, 10) >>> plt.legend() >>> plt.title(r'Modified Bessel function of the second kind $K_n(x)$') >>> plt.show()
Calculate for a single value at multiple orders:
>>> kn([4, 5, 6], 1) array([ 44.23241585, 360.9605896 , 3653.83831186])