26 Numerics library [numerics]

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

26.9.5 Mathematical special functions [sf.cmath]

26.9.5.10 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);

1

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.

2

Returns: \[% \mathsf{N}_\nu(x) = \left\{ \begin{array}{cl} \displaystyle \frac{\mathsf{J}_\nu(x) \cos \nu\pi - \mathsf{J}_{-\nu}(x)} {\sin \nu\pi }, & \mbox{for $x \ge 0$ and non-integral $\nu$} \\ \\ \displaystyle \lim_{\mu \rightarrow \nu} \frac{\mathsf{J}_\mu(x) \cos \mu\pi - \mathsf{J}_{-\mu}(x)} {\sin \mu\pi }, & \mbox{for $x \ge 0$ and integral $\nu$} \end{array} \right. \] where nu is nu and x is x.

3

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