26 Numerics library [numerics]

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

26.8.6 Mathematical special functions [sf.cmath]

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

double       cyl_bessel_i(double nu, double 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) = 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,

where ν is nu and x is x.

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