naginterfaces.library.specfun.kelvin_​ker_​vector

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

kelvin_ker_vector returns an array of values for the Kelvin function .

For full information please refer to the NAG Library document for s19aq

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s19aqf.html

Parameters
xfloat, array-like, shape

The argument of the function, for .

Returns
ffloat, ndarray, shape

, the function values.

ivalidint, ndarray, shape

contains the error code for , for .

No error.

is too large, the result underflows. contains zero. The threshold value is the same as for = 1 in kelvin_ker().

, the function is undefined. contains .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

On entry, at least one value of was invalid.

Check for more information.

Notes

kelvin_ker_vector evaluates 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:

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