naginterfaces.library.specfun.kelvin_​ker¶

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

kelvin_ker returns a value for the Kelvin function .

For full information please refer to the NAG Library document for s19ac

https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/s/s19acf.html

Parameters
xfloat

The argument of the function.

Returns
kerfloat

The value of the function at .

Raises
NagValueError
(errno )

On entry, . The function returns zero.

Constraint: .

is too large, the result underflows and the function returns zero.

(errno )

On entry, .

Constraint: .

The function is undefined and returns zero.

Notes

kelvin_ker evaluates an approximation to the Kelvin function .

Note: for the function is undefined and at it is infinite so we need only consider .

The function is based on several Chebyshev expansions:

For ,

where , and are expansions in the variable .

For ,

where is an expansion in the variable .

For ,

where , and and are expansions in the variable .

When is sufficiently close to zero, the result is computed as

and when is even closer to zero, simply as .

For large , is asymptotically given by and this becomes so small that it cannot be computed without underflow and the function fails.

References

NIST Digital Library of Mathematical Functions