{"paper":{"title":"A sampling-based approximation of the complex error function and its implementation without poles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"B. M. Quine, R. K. Jagpal, S. M. Abrarov","submitted_at":"2018-02-16T20:42:05Z","abstract_excerpt":"Recently we developed a new sampling methodology based on incomplete cosine expansion of the sinc function and applied it in numerical integration in order to obtain a rational approximation for the complex error function $w\\left(z \\right) = e^{- {z^2}}\\left(1 + \\frac{2i}{\\sqrt \\pi}\\int_0^z e^{t^2}dt\\right),$ where $z = x + iy$. As a further development, in this work we show how this sampling-based rational approximation can be transformed into alternative form for efficient computation of the complex error function $w\\left(z \\right)$ at smaller values of the imaginary argument $y=\\operatornam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06077","kind":"arxiv","version":3},"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"}