29 Numerics library [numerics]

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

29.9.5 Mathematical special functions [sf.cmath] 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.


Kν(x)=(π/2)iν+1(Jν(ix)+iNν(ix))=⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪π2Iν(x)Iν(x)sinνπ,for x0 and non-integral νπ2limμνIμ(x)Iμ(x)sinμπ,for x0 and integral ν

where ν is nu and x is x.

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