26 Numerics library [numerics]
26.9 Mathematical functions for floating-point types [c.math]
26.9.5 Mathematical special functions [sf.cmath]
26.9.5.9 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:
![\[%
\mathsf{K}_\nu(x) =
(\pi/2)\mathrm{i}^{\nu+1} ( \mathsf{J}_\nu(\mathrm{i}x)
+ \mathrm{i} \mathsf{N}_\nu(\mathrm{i}x)
)
=
\left\{
\begin{array}{cl}
\displaystyle
\frac{\pi}{2}
\frac{\mathsf{I}_{-\nu}(x) - \mathsf{I}_{\nu}(x)}
{\sin \nu\pi },
& \mbox{for $x \ge 0$ and non-integral $\nu$}
\\
\\
\displaystyle
\frac{\pi}{2}
\lim_{\mu \rightarrow \nu} \frac{\mathsf{I}_{-\mu}(x) - \mathsf{I}_{\mu}(x)}
{\sin \mu\pi },
& \mbox{for $x \ge 0$ and integral $\nu$}
\end{array}
\right.
\]](math/136333380479809245.png)
where
nu is nu and
x is x.