26 Numerics library [numerics]
26.9 Mathematical functions for floating-point types [c.math]
26.9.5 Mathematical special functions [sf.cmath]
26.9.5.2 Associated Legendre functions [sf.cmath.assoc_legendre]
double assoc_legendre(unsigned l, unsigned m, double x);
float assoc_legendref(unsigned l, unsigned m, float x);
long double assoc_legendrel(unsigned l, unsigned m, long double x);
Effects: These functions compute the associated Legendre functions of their respective arguments l, m, and x.
Returns:
![\[%
\mathsf{P}_\ell^m(x) =
(1 - x^2) ^ {m/2}
\:
\frac{ \mathsf{d} ^ m}
{ \mathsf{d}x ^ m} \, \mathsf{P}_\ell(x),
\quad \mbox{for $|x| \le 1$}
\]](math/7280053638369289593.png)
where
l is l,
m is m, and
x is x.