Recent content by Nurdan

It is known that \sum\limits_{k = 0}^\infty {\frac{{N^k }}{{k!}}} = e^N I am looking for any asymptotic approximation which gives \sum\limits_{k = 0}^M {\frac{{N^k }}{{k!}}} = ? where M\leq N an integer. This is not an homework

It is ok. I know the proof of this but still i need some approximations

My empiric results show that if M=N the answer is (e^N)/2. I am looking for any asymptotic approach that gives the solution as M=N.

It is known that \[\sum\limits_{k = 0}^\infty {\frac{{N^k }} {{k!}}} = e^N \] My question is \[\sum\limits_{k = 0}^M {\frac{{N^k }} {{k!}}} = ? \] where $M\leq N$ an integer. This is not an homework