26 Numerics library [numerics]

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

26.9.5 Mathematical special functions [sf.cmath]

26.9.5.7 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);

1

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

2

Returns: \[% \mathsf{I}_\nu(x) = \mathrm{i}^{-\nu} \mathsf{J}_\nu(\mathrm{i}x) = \sum_{k=0}^\infty \frac{(x/2)^{\nu+2k}} {k! \: \Gamma(\nu+k+1)}, \quad \mbox{for $x \ge 0$} \] where nu is nu and x is x.

3

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