{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:XQGFUM4ELZ4KOO2W77NAAN36KR","short_pith_number":"pith:XQGFUM4E","schema_version":"1.0","canonical_sha256":"bc0c5a33845e78a73b56ffda00377e5447b6c73bbe579d90e44a50bff13e5a7c","source":{"kind":"arxiv","id":"1712.08799","version":1},"attestation_state":"computed","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("},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.08799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-12-23T16:19:12Z","cross_cats_sorted":[],"title_canon_sha256":"846e618a466636663c7c9f3b0533ff1719dd357d0ce2e797ad05768da8519894","abstract_canon_sha256":"f98449ee71ead29227c5591d619e704a23851fec9baa3951b1a61396f59916f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:16.775422Z","signature_b64":"OqhvHJFUiBIpuCv74ghy7NXOe1Rm0YvnKRsgmqx0dH+kLmcQadqAroIpxIYz+qItX02LqxGrviXoeN4An1r/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc0c5a33845e78a73b56ffda00377e5447b6c73bbe579d90e44a50bff13e5a7c","last_reissued_at":"2026-05-18T00:27:16.775000Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:16.775000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 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