{"paper":{"title":"Error estimates for the Gregory-Leibniz series and the alternating harmonic series using Dalzell integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Diego Rattaggi","submitted_at":"2018-08-30T17:01:46Z","abstract_excerpt":"The computation of Dalzell integrals $\\int_0^1 \\frac{x^m (1-x)^n}{1+x^2} \\, dx > 0$ gives new error estimates for the partial sums of the Gregory-Leibniz series $1 - \\frac{1}{3} + \\frac{1}{5} - \\frac{1}{7} \\pm \\ldots$ and for the alternating harmonic series $1 - \\frac{1}{2} + \\frac{1}{3} - \\frac{1}{4} \\pm \\ldots$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00998","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"}