# Laguerre L

The Laguerre polynomial of order $n$, $L_n$, is given by $$L_n(x) = \displaystyle\sum_{k=0}^n \dfrac{(-1)^kn!}{(n-k)!(k!)^2}x^k.$$
The first few Laguerre polynomials are given by $$\begin{array}{ll} L_0(x) &= 1 \\ L_1(x) &= -x+1 \\ L_2(x) &= \dfrac{1}{2}(x^2-4x+2) \\ L_3(x) &= \dfrac{1}{6}(-x^3+9x^2-18x+6) \\ L_4(x) &= \dfrac{1}{24}(x^4-16x^3+72x^2-96x+24)\\ \vdots \end{array}$$