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arXiv · 1508.07276

Asymptotics of alternating harmonic series with attenuation

Sergey Sadov
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Abstract

We find the asymptotics of the series $\sum_{n=1}^\infty (-1)^n n^{-1} \exp(-t/n)$ as $t\to+\infty$. The answer is an oscillating function of $t$ dominated by $\exp(-(2πt)^{1/2})$. The intermediate step is to find the asymptotics of the two-dimensional Fourier transform $\hat F(ξ)$ of the function $F(x)=(1+\exp(\|x\|^2))^{-1}$ as $\|ξ\|\to\infty$.

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Sergey Sadov. 2015-08-28. Asymptotics of alternating harmonic series with attenuation. https://arxiv.org/abs/1508.07276

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