naginterfaces.library.specfun.bessel_​i0_​scaled_​vector

naginterfaces.library.specfun.bessel_i0_scaled_vector(x)

bessel_i0_scaled_vector returns an array of values of the scaled modified Bessel function $e^{-\left|x\right|}{I}_0\left(x\right)$.

For full information please refer to the NAG Library document for s18cs

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/s/s18csf.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 $\left(n\right)$

$e^{-\left|x_i\right|}{I}_0\left(x_i\right)$, the function values.

Warns

NagAlgorithmicWarning

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

Notes

bessel_i0_scaled_vector evaluates an approximation to $e^{-\left|x_i\right|}{I}_0\left(x_i\right)$, where $I_0$ is a modified Bessel function of the first kind for an array of arguments $x_{\text{i}}$, for $\text{i}=1,2,\dots ,n$. The scaling factor $e^{-\left|x\right|}$ removes most of the variation in $I_0\left(x\right)$.

The function uses the same Chebyshev expansions as bessel_i0_real_vector(), which returns an array of the unscaled values of $I_0\left(x\right)$.

References

NIST Digital Library of Mathematical Functions