#### Vol. 14, No. 5, 2021

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On the coefficients in an asymptotic expansion of $(1+1/x)^x$

### T. M. Dunster and Jessica M. Perez

Vol. 14 (2021), No. 5, 775–781
##### Abstract

The function $g\left(x\right)={\left(1+1∕x\right)}^{x}$ has the well-known limit $e$ as $x\to \infty$. The coefficients ${c}_{j}$ in an asymptotic expansion for $g\left(x\right)$ are considered. A simple recursion formula is derived, and then using Cauchy’s integral formula the coefficients are approximated for large $j$. From this it is shown that $|{c}_{j}|\to 1$ as $j\to \infty$.

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