# scipy.special.k0e#

scipy.special.k0e(x, out=None) = <ufunc 'k0e'>#

Exponentially scaled modified Bessel function K of order 0

Defined as:

```k0e(x) = exp(x) * k0(x).
```
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 0 at x.

`kv`

Modified Bessel function of the second kind of any order

`k0`

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 `k0e`. `k0e` is useful for large arguments: for these, `k0` easily underflows.

References



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

Examples

In the following example `k0` returns 0 whereas `k0e` still returns a useful finite number:

```>>> from scipy.special import k0, k0e
>>> k0(1000.), k0e(1000)
(0., 0.03962832160075422)
```

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

```>>> import numpy as np
>>> k0e(np.array([0.5, 2., 3.]))
array([1.52410939, 0.84156822, 0.6977616 ])
```

Plot the function from 0 to 10.

```>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots()
>>> x = np.linspace(0., 10., 1000)
>>> y = k0e(x)
>>> ax.plot(x, y)
>>> plt.show()
```