24 Numerics library [numerics]

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

24.9.5 Mathematical special functions [sf.cmath]

24.9.5.8 Cylindrical Bessel functions of the first kind [sf.cmath.cyl_bessel_j]

double       cyl_bessel_j(double nu, double x);
float        cyl_bessel_jf(float nu, float x);
long double  cyl_bessel_jl(long double nu, long double x);

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

Returns:

$J_{ν} (x) = \infty \sum k = 0 \frac{(- 1)^{k} (x / 2)^{ν + 2 k}}{k! Γ (ν + k + 1)}, for x \geq 0,$

where ν is nu and x is x.

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