29 Numerics library [numerics]

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

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.3 Associated Legendre functions [sf.cmath.assoc.legendre]

floating-point-type assoc_legendre(unsigned l, unsigned m, floating-point-type 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)

, where

P_{ℓ}^{m}

is given by Formula 29.23,

P_{ℓ}

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

\begin{matrix} P_{ℓ}^{m} (x) = (1 - x^{2})^{m / 2} \frac{d^{m}}{d x^{m}} P_{ℓ} (x), for | x | \leq 1 \\ (29.23) \end{matrix}

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