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://support.nag.com/numeric/nl/nagdoc_30.2/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