28 Numerics library [numerics]

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

28.7.6 Mathematical special functions [sf.cmath]

28.7.6.18 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) = \frac{1}{2^{ℓ} ℓ!} \frac{d^{ℓ}}{d x^{ℓ}} (x^{2} - 1)^{ℓ}, for | x | \leq 1,

where l is l and x is x.

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