It is known that [tex] \sum\limits_{k = 0}^\infty {\frac{{N^k }}{{k!}}} = e^N[/tex] I am looking for any asymptotic approximation which gives [tex] \sum\limits_{k = 0}^M {\frac{{N^k }}{{k!}}} = ? [/tex] where [tex]M\leq N[/tex] an integer. This is not an homework
I'm only being a little facetious if I point out that the sum is asymptotically equal to e^N. Want more accuracy? It's better approximated by e^N-[x^(N+1)]/(N+1)!