29 Numerics library [numerics]

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

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.18 Legendre polynomials [sf.cmath.legendre]

floating-point-type legendre(unsigned l, floating-point-type 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:

P_{ℓ} (x)

, where

P_{ℓ}

is given by Formula 29.38, l is l, and x is x.

\begin{matrix} P_{ℓ} (x) = \frac{1}{2^{ℓ} ℓ!} \frac{d^{ℓ}}{d x^{ℓ}} (x^{2} - 1)^{ℓ}, for | x | \leq 1 \\ (29.38) \end{matrix}

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