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.

See also

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 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])