{"paper":{"title":"A Short Tale of Long Tail Integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.CP"],"primary_cat":"math.NA","authors_text":"Pavel V. Shevchenko, Xiaolin Luo","submitted_at":"2010-05-11T03:12:16Z","abstract_excerpt":"Integration of the form $\\int_a^\\infty {f(x)w(x)dx} $, where $w(x)$ is either $\\sin (\\omega {\\kern 1pt} x)$ or $\\cos (\\omega {\\kern 1pt} x)$, is widely encountered in many engineering and scientific applications, such as those involving Fourier or Laplace transforms. Often such integrals are approximated by a numerical integration over a finite domain $(a,\\,b)$, leaving a truncation error equal to the tail integration $\\int_b^\\infty {f(x)w(x)dx} $ in addition to the discretization error. This paper describes a very simple, perhaps the simplest, end-point correction to approximate the tail inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1705","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"}