29 Numerics library [numerics]

29.7 Mathematical functions for floating-point types [c.math]

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.8 Regular modified cylindrical Bessel functions [sf.cmath.cyl.bessel.i]

floating-point-type cyl_bessel_i(floating-point-type nu, floating-point-type x);
float        cyl_bessel_if(float nu, float x);
long double  cyl_bessel_il(long double nu, long double x);

Effects: These functions compute the regular modified cylindrical Bessel functions of their respective arguments nu and x.

Returns:

I_{ν} (x)

, where

I_{ν}

is given by Formula 29.28, ν is nu, and x is x.

\begin{matrix} I_{ν} (x) = i^{- ν} J_{ν} (i x) = \infty \sum k = 0 \frac{(x / 2)^{ν + 2 k}}{k! Γ (ν + k + 1)}, for x \geq 0 \\ (29.28) \end{matrix}

Remarks: The effect of calling each of these functions is implementation-defined if nu >= 128.