3.5.1.3.5 bessel_i_nu

Definition:

\(bessel\_i\_nu = bessel\_i\_nu(x,nu)\) evaluates an approximation to the modified Bessel function of the first kind I\(\nu\)/4 (x), where the order v=-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\(\nu\)/4 (0)=0 when v>0. For negative orders the formula \(I_{-v/4}(x)=I_{v/4}(x)+\frac{2}{\pi}\sin\left(\frac{\pi v}{4}\right)K_{v/4}(x)\) is used.

For more information please review the s18eec function in the NAG document.

Parameters:

x (input,double)

The argument x of the function.

Constraints:

\(x>0.0\) when \(nu<0\),

\(x\geq 0.0\) when \(nu>0\).

nu (input,int)

The argument v of the function.

Constraints:

\(1\leq abs(nu)\leq 3\).

bessel_i_nu (output,double)

Approximation of the modified Bessel function of the first kind.