{"paper":{"title":"On a continued fraction expansion for Euler's constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood","submitted_at":"2010-10-07T12:57:23Z","abstract_excerpt":"Recently, A. I. Aptekarev and his collaborators found a sequence of rational approximations to Euler's constant $\\gamma$ defined by a third-order homogeneous linear recurrence. In this paper, we give a new interpretation of Aptekarev's approximations in terms of Meijer $G$-functions and hypergeometric-type series. This approach allows us to describe a very general construction giving linear forms in 1 and $\\gamma$ with rational coefficients. Using this construction we find new rational approximations to $\\gamma$ generated by a second-order inhomogeneous linear recurrence with polynomial coeffi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.1420","kind":"arxiv","version":3},"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"}