scipy.special.bei

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

Kelvin function bei.

Defined as

\[\mathrm{bei}(x) = \Im[J_0(x e^{3 \pi i / 4})]\]

where \(J_0\) is the Bessel function of the first kind of order zero (see jv). 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

ber

the corresponding real part

beip

the derivative of bei

jv

Bessel function of the first kind

References

dlmf

NIST, Digital Library of Mathematical Functions, https://dlmf.nist.gov/10.61

Examples

It can be expressed using Bessel functions.

>>> import scipy.special as sc
>>> x = np.array([1.0, 2.0, 3.0, 4.0])
>>> sc.jv(0, x * np.exp(3 * np.pi * 1j / 4)).imag
array([0.24956604, 0.97229163, 1.93758679, 2.29269032])
>>> sc.bei(x)
array([0.24956604, 0.97229163, 1.93758679, 2.29269032])