{"paper":{"title":"Asymptotics of a class of integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A.G.Ramm","submitted_at":"2013-02-02T15:54:45Z","abstract_excerpt":"Consider an integral $I(s):=\\int_0^T e^{-s(x^2-icx)}dx$, where $c>0$ and $T>0$ are arbitrary positive constants. It is proved that $I(s)\\sim \\frac{i}{sc}$ as $s\\to +\\infty$. The asymptotic behavior of the integral $J(s):=\\int_0^Te^{s(x^2+icx)}dx$ is also derived. One has $J(s)\\sim \\frac{e^{sT^2+iscT}}{s(2T+ic)}$ as $s\\to +\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0391","kind":"arxiv","version":2},"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"}