# 3.5.1.3.6 Bessel_i_nu_scaled

## Definition:

$i\_nu\_scaled = bessel\_i\_nu\_scaled(x,nu)$ evaluates an approximation to the modified Bessel function of the first kind $e^{-x}I_{\frac \nu 4}(x)$, where the order =-3, -2, -1, 1, 2 or 3 and x is real and positive. For positive orders it may also be called with x=0, since $I_{\frac \nu 4}(0)=0$ when $\nu$ > 0. For negative orders the formula

$I_{\frac{-\nu }4}(x)=I_{\frac \upsilon 4}(x)+\frac 2\pi \sin (\frac{\pi \upsilon }4)K_{\frac \upsilon 4}(x)$

is used prior to multiplication by the scale factor $e^{-x}$.

## Parameters:

x (input, double)
The argument x of the function.
Constraints:
x>0.0 when nu<0,
x???0.0 when nu>0.
$nu$ (input, int)
The argument $\nu$ of the function.
Constraints:
$1\leq abs(nu)\leq 3$
$i\_nu\_scaled$ (output, double)
Approximation of the modified Bessel function of the first kind.