29 Numerics library [numerics]

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

29.7.6 Mathematical special functions [sf.cmath]

29.7.6.17 Laguerre polynomials [sf.cmath.laguerre]

floating-point-type laguerre(unsigned n, floating-point-type x);
float        laguerref(unsigned n, float x);
long double  laguerrel(unsigned n, long double x);

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

Returns:

L_{n} (x)

, where

L_{n}

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

\begin{matrix} L_{n} (x) = \frac{e^{x}}{n!} \frac{d^{n}}{d x^{n}} (x^{n} e^{- x}), for x \geq 0 \\ (29.37) \end{matrix}

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