26 Numerics library [numerics]
26.9 Mathematical functions for floating-point types [c.math]
26.9.5 Mathematical special functions [sf.cmath]
26.9.5.17 Legendre polynomials [sf.cmath.legendre]
double legendre(unsigned l, double x);
float legendref(unsigned l, float x);
long double legendrel(unsigned l, long double x);
Effects: These functions compute the Legendre polynomials of their respective arguments l and x.
Returns:
![\[%
\mathsf{P}_\ell(x) =
\frac{1}
{2^\ell \, \ell!}
\frac{ \mathsf{d} ^ \ell}
{ \mathsf{d}x ^ \ell} \, (x^2 - 1) ^ \ell,
\quad \mbox{for $|x| \le 1$}
\]](math/5890542632393796283.png)
where
l is l and
x is x.