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

The function $g (x) = (1 + 1 / x)^{x}$ has the well-known limit $e$ as $x \to \infty$ . The coefficients $c_{j}$ in an asymptotic expansion for $g (x)$ 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 $j \to \infty$ .

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

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

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

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

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

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

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