scipy.special.kei¶
-
scipy.special.
kei
(x, out=None) = <ufunc 'kei'>¶ Kelvin function kei.
Defined as
\[\mathrm{kei}(x) = \Im[K_0(x e^{\pi i / 4})]\]where \(K_0\) is the modified Bessel function of the second kind (see
kv
). See [dlmf] for more details.- Parameters
- xarray_like
Real argument.
- outndarray, optional
Optional output array for the function results.
- Returns
- scalar or ndarray
Values of the Kelvin function.
See also
References
- dlmf
NIST, Digital Library of Mathematical Functions, https://dlmf.nist.gov/10.61
Examples
It can be expressed using the modified Bessel function of the second kind.
>>> import scipy.special as sc >>> x = np.array([1.0, 2.0, 3.0, 4.0]) >>> sc.kv(0, x * np.exp(np.pi * 1j / 4)).imag array([-0.49499464, -0.20240007, -0.05112188, 0.0021984 ]) >>> sc.kei(x) array([-0.49499464, -0.20240007, -0.05112188, 0.0021984 ])