# naginterfaces.library.specfun.bessel_​k0_​real_​vector¶

naginterfaces.library.specfun.bessel_k0_real_vector(x)[source]

bessel_k0_real_vector returns an array of values of the modified Bessel function .

For full information please refer to the NAG Library document for s18aq

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s18aqf.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 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

bessel_k0_real_vector evaluates an approximation to the modified Bessel function of the second kind for an array of arguments , for .

Note: is undefined for and the function will fail for such arguments.

The function is based on five Chebyshev expansions:

For ,

For ,

For ,

For ,

For near zero, , where denotes Euler’s constant. This approximation is used when is sufficiently small for the result to be correct to machine precision.

For large , where there is a danger of underflow due to the smallness of , the result is set exactly to zero.

References

NIST Digital Library of Mathematical Functions