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

ker: the corresponding real part
keip: the derivative of kei
kv: modified Bessel function of the second kind

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 numpy as np
>>> 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 ])