29 Numerics library [numerics]

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

29.9.5 Mathematical special functions [sf.cmath] 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.


Nν(x)=⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪Jν(x)cosνπJν(x)sinνπ,for x0 and non-integral νlimμνJμ(x)cosμπJμ(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.