scipy.special.ker#

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

Kelvin function ker.

Defined as

$\mathrm{ker}(x) = \Re[K_0(x e^{\pi i / 4})]$

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.

kei

the corresponding imaginary part

kerp

the derivative of ker

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)).real
array([ 0.28670621, -0.04166451, -0.06702923, -0.03617885])
>>> sc.ker(x)
array([ 0.28670621, -0.04166451, -0.06702923, -0.03617885])