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 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 ])