24 Numerics library [numerics]

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

24.9.5 Mathematical special functions [sf.cmath]

24.9.5.2 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:

$P_{ℓ}^{m} (x) = (1 - x^{2})^{m / 2} \frac{d^{m}}{d x^{m}} P_{ℓ} (x), for | x | \leq 1,$

where l is l, m is m, and x is x.

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