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 numpy as np
>>> 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])