naginterfaces.library.specfun.kelvin_​bei

naginterfaces.library.specfun.kelvin_bei(x)[source]

kelvin_bei returns a value for the Kelvin function .

For full information please refer to the NAG Library document for s19ab

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s19abf.html

Parameters
xfloat

The argument of the function.

Returns
beifloat

The value of the function at .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

is too large for an accurate result to be returned and the function returns zero.

Notes

kelvin_bei evaluates an approximation to the Kelvin function .

Note: , so the approximation need only consider .

The function is based on several Chebyshev expansions:

For ,

For ,

where , ,

and , , , and are expansions in the variable .

When is sufficiently close to zero, the result is computed as . If this result would underflow, the result returned is .

For large , there is a danger of the result being totally inaccurate, as the error amplification factor grows in an essentially exponential manner;, therefore, the function must fail.

References

NIST Digital Library of Mathematical Functions