{"paper":{"title":"Sharp Estimates of the Generalized Euler-Mascheroni Constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bo-Wen Han, Ti-Ren Huang, Xiao-Yan Ma, You-Ling Liu","submitted_at":"2017-12-23T16:19:12Z","abstract_excerpt":"Let $a\\in (0, \\infty)$, $\\gamma(a)$ be the Generalized Euler-Mascheroni Constant, and let \\begin{align*} &x_n=\\frac1a+\\frac{1}{a+1}+\\cdots+\\frac{1}{a+n-1}-\\ln\\frac{a+n}{a},\\\\ &y_n=\\frac1a+\\frac{1}{a+1}+\\cdots+\\frac{1}{a+n-1}-\\ln\\frac{a+n-1}{a}. \\end{align*} In this paper, we determine the best possible constants $\\alpha_i, \\beta_i (i=1,2,3,4)$ such that the following inequalities \\begin{align*} \\frac{1}{2(n+a)-\\alpha_1}\\leq &\\gamma(a)-x_n< \\frac{1}{2(n+a)-\\beta_1},\\\\ \\frac{1}{2(n+a)-\\alpha_2}\\leq &y_n-\\gamma(a)< \\frac{1}{2(n+a)-\\beta_2},\\\\ \\frac{1}{2(n+a)}+\\frac{\\alpha_3}{(n+a)^2}\\leq &\\gamma("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08799","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"}