{"paper":{"title":"Asymptotics of alternating harmonic series with attenuation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Sergey Sadov","submitted_at":"2015-08-28T16:53:25Z","abstract_excerpt":"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 $\\exp(-(2\\pi t)^{1/2})$. The intermediate step is to find the asymptotics of the two-dimensional Fourier transform $\\hat F(\\xi)$ of the function $F(x)=(1+\\exp(\\|x\\|^2))^{-1}$ as $\\|\\xi\\|\\to\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07276","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}