/sci/ - Science & Math

I know this function F(x) converges,
because terms of [math]e^x[/math] converge,
and [math]L_n(x)[/math] is decreasing, duh
but how do I graph this doggie?
[math]\displaystyle F(x)= \lim_{n \rightarrow \infty}F_n(x)=e^{-x}[L_1(x)+xL_2(x)+\frac{x^2}{2!}L_3(x)+ \cdots+\frac{x^n}{n!}L_{n+1}(x)][/math]
where [math]n \epsilon \mathbb{N}[/math]
and [math]x \geq 0[/math]
and [math]L_0(x)=x[/math]
and [math]L_n(x)= \ln(L_{n-1}(x)+1)[/math]