{"paper":{"title":"Sharp bounds for harmonic numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bai-Ni Guo, Feng Qi","submitted_at":"2010-02-20T07:56:38Z","abstract_excerpt":"In the paper, we first survey some results on inequalities for bounding harmonic numbers or Euler-Mascheroni constant, and then we establish a new sharp double inequality for bounding harmonic numbers as follows: For $n\\in\\mathbb{N}$, the double inequality -\\frac{1}{12n^2+{2(7-12\\gamma)}/{(2\\gamma-1)}}\\le H(n)-\\ln n-\\frac1{2n}-\\gamma<-\\frac{1}{12n^2+6/5} is valid, with equality in the left-hand side only when $n=1$, where the scalars $\\frac{2(7-12\\gamma)}{2\\gamma-1}$ and $\\frac65$ are the best possible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3856","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"}