# naginterfaces.library.specfun.kelvin_​kei_​vector¶

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

kelvin_kei_vector returns an array of values for the Kelvin function .

For full information please refer to the NAG Library document for s19ar

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s19arf.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_kei().

, the function is undefined. contains .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

On entry, at least one value of was invalid.

Notes

kelvin_kei_vector evaluates an approximation to the Kelvin function for an array of arguments , for .

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