kelvin_ker_vectorreturns an array of values for the Kelvin function .
For full information please refer to the NAG Library document for s19aq
- xfloat, array-like, shape
The argument of the function, for .
- ffloat, ndarray, shape
, the function values.
- ivalidint, ndarray, shape
contains the error code for , for .
is too large, the result underflows. contains zero. The threshold value is the same as for = 1 in
, the function is undefined. contains .
- (errno )
On entry, .
- (errno )
On entry, at least one value of was invalid.
Check for more information.
kelvin_ker_vectorevaluates an approximation to the Kelvin function for an array of arguments , for .
Note: for the function is undefined and at it is infinite so we need only consider .
The function is based on several Chebyshev expansions:
where , and are expansions in the variable .
where is an expansion in the variable .
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.
NIST Digital Library of Mathematical Functions