{"paper":{"title":"Elementary proofs of generalized continued fraction formulae for $e$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.HO"],"primary_cat":"math.NT","authors_text":"Zhentao Lu","submitted_at":"2019-07-12T03:35:54Z","abstract_excerpt":"In this short note we prove two elegant generalized continued fraction formulae $$e= 2+\\cfrac{1}{1+\\cfrac{1}{2+\\cfrac{2}{3+\\cfrac{3}{4+\\ddots}}}}$$ and $$e= 3+\\cfrac{-1}{4+\\cfrac{-2}{5+\\cfrac{-3}{6+\\cfrac{-4}{7+\\ddots}}}}$$ using elementary methods. The first formula is well-known, and the second one is newly-discovered in arXiv:1907.00205 [cs.LG]. We then explore the possibility of automatic verification of such formulae using computer algebra systems (CAS's)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05563","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"}