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 \(e^{-x}\).

For more information please review the s18ecc function in the NAG document.

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.