naginterfaces.library.specfun.kelvin_​bei_​vector

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

kelvin_bei_vector returns an array of values for the Kelvin function .

For full information please refer to the NAG Library document for s19ap

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s19apf.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 for an accurate result to be returned. contains zero. The threshold value is the same as for = 1 in kelvin_bei().

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

On entry, at least one value of was invalid.

Check for more information.

Notes

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

Note: , so the approximation need only consider .

The function is based on several Chebyshev expansions:

For ,

For ,

where , ,

and , , , and are expansions in the variable .

When is sufficiently close to zero, the result is computed as . If this result would underflow, the result returned is .

For large , there is a danger of the result being totally inaccurate, as the error amplification factor grows in an essentially exponential manner;, therefore, the function must fail.

References

NIST Digital Library of Mathematical Functions