26 Numerics library [numerics]
26.9 Mathematical functions for floating-point types [c.math]
26.9.5 Mathematical special functions [sf.cmath]
26.9.5.20 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).
Returns:
Yℓm(θ, 0)
where
![\[%
\mathsf{Y}_\ell^m(\theta, \phi) =
(-1)^m \left[ \frac{(2 \ell + 1)}
{4 \pi}
\frac{(\ell - m)!}
{(\ell + m)!}
\right]^{1/2}
\mathsf{P}_\ell^m
( \cos\theta ) e ^ {i m \phi},
\quad \mbox{for $|m| \le \ell$}
\]](math/7858298838263879409.png)
and
l is l,
m is m, and
theta is theta.
See also [sf.cmath.assoc_legendre].