3.5.2.5.6 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.