29 Numerics library [numerics]

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

29.9.5 Mathematical special functions [sf.cmath]

29.9.5.10 Cylindrical Neumann functions [sf.cmath.cyl_neumann]

double       cyl_neumann(double nu, double x);
float        cyl_neumannf(float nu, float x);
long double  cyl_neumannl(long double nu, long double x);

Effects: These functions compute the cylindrical Neumann functions, also known as the cylindrical Bessel functions of the second kind, of their respective arguments nu and x.

Returns:

$N_{ν} (x) = ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} \frac{J_{ν} (x) cos ν π - J_{- ν} (x)}{sin ν π}, & for x \geq 0 and non-integral ν lim_{μ \to ν} \frac{J_{μ} (x) cos μ π - J_{- μ} (x)}{sin μ π}, & for x \geq 0 and integral ν \end{matrix}$

where ν is nu and x is x.

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