29 Numerics library [numerics]

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

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.2 Associated Laguerre polynomials [sf.cmath.assoc.laguerre]

floating-point-type assoc_laguerre(unsigned n, unsigned m, floating-point-type x);
float        assoc_laguerref(unsigned n, unsigned m, float x);
long double  assoc_laguerrel(unsigned n, unsigned m, long double x);

Effects: These functions compute the associated Laguerre polynomials of their respective arguments n, m, and x.

Returns:

L_{n}^{m} (x)

, where

L_{n}^{m}

is given by Formula 29.22,

L_{n + m}

is given by Formula 29.37, n is n, m is m, and x is x.

\begin{matrix} L_{n}^{m} (x) = (- 1)^{m} \frac{d^{m}}{d x^{m}} L_{n + m} (x), for x \geq 0 \\ (29.22) \end{matrix}

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