naginterfaces.library.specfun.kelvin_​kei

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

kelvin_kei returns a value for the Kelvin function .

For full information please refer to the NAG Library document for s19ad

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s19adf.html

Parameters
xfloat

The argument of the function.

Returns
keifloat

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_kei evaluates an approximation to the Kelvin function .

Note: for the function is undefined, 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 .

For , the function is undefined, and hence the function fails and returns zero.

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