naginterfaces.library.specfun.bessel_​i0_​scaled

naginterfaces.library.specfun.bessel_i0_scaled(x)

bessel_i0_scaled returns a value 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 s18ce

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/s/s18cef.html

Parameters

xfloat

The argument $x$ of the function.

Returns

si0float

The value of the function at $x$.

Notes

bessel_i0_scaled evaluates an approximation to $e^{-\left|x\right|}{I}_0\left(x\right)$, where $I_0$ is a modified Bessel function of the first kind. 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(), which returns the unscaled value of $I_0\left(x\right)$.

References

NIST Digital Library of Mathematical Functions