29 Numerics library [numerics]

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

29.9.5 Mathematical special functions [sf.cmath] Spherical associated Legendre functions [sf.cmath.sph_legendre]

double sph_legendre(unsigned l, unsigned m, double theta); float sph_legendref(unsigned l, unsigned m, float theta); long double sph_legendrel(unsigned l, unsigned m, long double theta);

Effects: These functions compute the spherical associated Legendre functions of their respective arguments l, m, and theta (theta measured in radians).




Ym(θ,ϕ)=(1)m[(2+1)4π(m)!(+m)!]1/2Pm(cosθ)eimϕ,for |m|

and l is l, m is m, and θ is theta.

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