29 Numerics library [numerics]

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

29.9.5 Mathematical special functions [sf.cmath]

29.9.5.9 Irregular modified cylindrical Bessel functions [sf.cmath.cyl_bessel_k]

double cyl_bessel_k(double nu, double x); float cyl_bessel_kf(float nu, float x); long double cyl_bessel_kl(long double nu, long double x);

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

Returns:

$K_{ν} (x) = (π / 2) i^{ν + 1} (J_{ν} (i x) + i N_{ν} (i x)) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{π}{2} \frac{I_{- ν} (x) - I_{ν} (x)}{sin ν π}, & for x \geq 0 and non-integral ν \frac{π}{2} lim μ \to ν \frac{I_{- μ} (x) - I_{μ} (x)}{sin μ π}, & for x \geq 0 and integral ν \end{matrix}$

where ν is nu and x is x.

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