naginterfaces.library.specfun.bessel_​k1_​scaled_​vector

naginterfaces.library.specfun.bessel_k1_scaled_vector(x)

bessel_k1_scaled_vector returns an array of values of the scaled modified Bessel function $e^x{K}_1\left(x\right)$.

For full information please refer to the NAG Library document for s18cr

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/s/s18crf.html

Parameters

xfloat, array-like, shape $\left(n\right)$

The argument $x_{\text{i}}$ of the function, for $\text{i}=1,2,\dots ,n$.

Returns

ffloat, ndarray, shape $\left(n\right)$

$e^{x_i}{K}_1\left(x_i\right)$, the function values.

ivalidint, ndarray, shape $\left(n\right)$

$ivalid[\text{i}-1]$ contains the error code for $x_{\text{i}}$, for $\text{i}=1,2,\dots ,n$.

$ivalid[i-1]=0$

No error.

$ivalid[i-1]=1$

On entry, $x_i\le 0.0$, $K_1\left(x_i\right)$ is undefined. $f[\text{i}-1]$ contains $0.0$.

$ivalid[i-1]=2$

$x_i$ is too close to zero, as determined by the value of the safe-range parameter machine.real_safe: there is a danger of causing overflow. $f[\text{i}-1]$ contains the reciprocal of the safe-range parameter.

Raises

NagValueError

(errno $2$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

Warns

NagAlgorithmicWarning

(errno $1$)

On entry, at least one value of $x$ was invalid.

Check $ivalid$ for more information.

Notes

bessel_k1_scaled_vector evaluates an approximation to $e^{x_i}{K}_1\left(x_i\right)$, where $K_1$ is a modified Bessel function of the second kind for an array of arguments $x_{\text{i}}$, for $\text{i}=1,2,\dots ,n$. 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_vector(), which returns an array of the unscaled values of $K_1\left(x\right)$.

References

NIST Digital Library of Mathematical Functions