naginterfaces.library.specfun.bessel_​k1_​scaled

naginterfaces.library.specfun.bessel_k1_scaled(x)

bessel_k1_scaled returns a value of the scaled modified Bessel function $e^x{K}_1\left(x\right)$.

For full information please refer to the NAG Library document for s18cd

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/s/s18cdf.html

Parameters

xfloat

The argument $x$ of the function.

Returns

sk1float

The value of the function at $x$.

Raises

NagValueError

(errno $1$)

On entry, $x=⟨value⟩$.

Constraint: $x>0.0$.

$K_1$ is undefined and the function returns zero.

(errno $2$)

On entry, $x=⟨value⟩$.

Constraint: $x>⟨value⟩$.

The function returns the value of the function at the smallest permitted value of the argument.

Notes

bessel_k1_scaled evaluates an approximation to $e^x{K}_1\left(x\right)$, where $K_1$ is a modified Bessel function of the second kind. The scaling factor $e^x$ removes most of the variation in $K_1\left(x\right)$.

The function uses the same Chebyshev expansions as bessel_k1_real(), which returns the unscaled value of $K_1\left(x\right)$.

References

NIST Digital Library of Mathematical Functions