{"paper":{"title":"Combinatorial identities involving harmonic numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Necdet Batir","submitted_at":"2018-06-08T08:37:59Z","abstract_excerpt":"In this work we prove a new combinatorial identity and applying it we establish many finite harmonic sum identities. Among many others, we prove that \\begin{equation*}\n  \\sum_{k=1}^{n}\\frac{(-1)^{k-1}}{k}\\binom{n}{k}H_{n-k}=H_n^2+\\sum_{k=1}^{n}\\frac{(-1)^{k}}{k^2\\binom{n}{k}}, \\end{equation*} and \\begin{equation*} \\sum_{k=1}^{n}\\frac{(-1)^{k-1}}{k^2}\\binom{n}{k}H_{n-k}=\\frac{H_n[H_n^2+H_n^{(2)}]}{2}-\\sum_{k=0}^{n-1}\\frac{(-1)^k[H_n-H_k]}{(k+1)(n-k)\\binom{n}{k}}. \\end{equation*} Almost all of our results are new, while a few of them recapture know results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03022","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"}