{"paper":{"title":"Euler's constant, q-logarithms, and formulas of Ramanujan and Gosper","license":"","headline":"","cross_cats":["math.CA"],"primary_cat":"math.NT","authors_text":"Jonathan Sondow (New York), Wadim Zudilin (Moscow)","submitted_at":"2003-04-02T13:53:58Z","abstract_excerpt":"The aim of the paper is to relate computational and arithmetic questions about Euler's constant $\\gamma$ with properties of the values of the $q$-logarithm function, with natural choice of $q$. By these means, we generalize a classical formula for $\\gamma$ due to Ramanujan, together with Vacca's and Gosper's series for $\\gamma$, as well as deduce irrationality criteria and tests and new asymptotic formulas for computing Euler's constant. The main tools are Euler-type integrals and hypergeometric series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0304021","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"}