# 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:
    x array_like

      Argument (float)

    out ndarray, optional

      Optional output array for the function values

  Returns:
    K scalar or ndarray

      Value of the exponentially scaled modified Bessel function K of order 0 at x.

  See also

  `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 [1] routine `k0e`. `k0e` is useful for large arguments: for these, `k0` easily underflows.

  References

  [1]

  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()