# naginterfaces.library.specfun.bessel_​k1_​real_​vector¶

naginterfaces.library.specfun.bessel_k1_real_vector(x)[source]

bessel_k1_real_vector returns an array of values of the modified Bessel function .

For full information please refer to the NAG Library document for s18ar

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/s/s18arf.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 .

is too small, there is a danger of overflow. contains zero. The threshold value is the same as for = 2 in bessel_k1_real().

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Warns
NagAlgorithmicWarning
(errno )

On entry, at least one value of was invalid.

Notes

bessel_k1_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, . This approximation is used when is sufficiently small for the result to be correct to machine precision. For very small it is impossible to calculate without overflow and the function must fail.

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