scipy.special.k1e — SciPy v1.15.2 Manual (original) (raw)

scipy.special.k1e(x, out=None) = <ufunc 'k1e'>#

Exponentially scaled modified Bessel function K of order 1

Defined as:

Parameters:

xarray_like

Argument (float)

outndarray, optional

Optional output array for the function values

Returns:

Kscalar or ndarray

Value of the exponentially scaled modified Bessel function K of order 1 at x.

See also

kv

Modified Bessel function of the second kind of any order

k1

Modified Bessel function of the second kind of order 1

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 k1e.

References

Examples

In the following example k1 returns 0 whereas k1e still returns a useful floating point number.

from scipy.special import k1, k1e k1(1000.), k1e(1000.) (0., 0.03964813081296021)

Calculate the function at several points by providing a NumPy array or list for x:

import numpy as np k1e(np.array([0.5, 2., 3.])) array([2.73100971, 1.03347685, 0.80656348])

Plot the function from 0 to 10.

import matplotlib.pyplot as plt fig, ax = plt.subplots() x = np.linspace(0., 10., 1000) y = k1e(x) ax.plot(x, y) plt.show()