Problem: find the asymptotic expansion of the following integral: $$I_n=\int_0^1\exp(x^n)dx$$ as $n \to \infty$. This expansion, while at first pedestrianseeming, turns out to have a very interesting set of coefficients. You can expand the exponential in a Taylor series quite accurately: $$\exp{\left ( x^n \right )} = 1 + x^n + \frac12 x^{2 n} + […]

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