These polynomials show up naturally in my work
$$
p\_n(x) = \sum\_{j=0}^n {n \choose j} \frac{(-x)^j}{j!}
$$
Does anyone know recognize if they belong to any class of well known polynomials. I am trying to compute
$$
\lim\_{n \rightarrow \infty} \int\_{R^2} f(|r|)e^{-\frac{a}{2}|x|^2} p\_n(a x) \, dx
$$
for some nice function f and $a > 0$. I think the limit should be 0.



Does anyone recognize these polynomials? Need to compute a riemann lebesgue type limit
Maple says $$\sum \_{j=0}^{n}{\frac {{n\choose j} \left( -z \right) ^{j}}{j!}}={L}\_n \left(z \right)$$ Laguerre polynomials. See <https://en.wikipedia.org/wiki/Laguerre_polynomials> and go down to "closed form".


