Algebraic properties of summation of exponential Taylor polynomials

Lingfeng Ao, Shaofang Hong

Let $n\ge 1$ be an integer and $e_n(x)$ denote the truncated exponential Taylor polynomial, i.e. $e_n(x)={\sum }_{i=0}^n\frac{x^i}{i!}$. A well-known theorem of Schur states that th…