scipy.special.ber#

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

Kelvin function ber.

Defined as

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

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

bei: the corresponding real part
berp: 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)).real
array([ 0.98438178,  0.75173418, -0.22138025, -2.56341656])
>>> sc.ber(x)
array([ 0.98438178,  0.75173418, -0.22138025, -2.56341656])