{"paper":{"title":"Rational approximations for values of the digamma function and a denominators conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Khodabakhsh Hessami Pilehrood, Tatiana Hessami Pilehrood","submitted_at":"2010-04-05T07:25:56Z","abstract_excerpt":"In 2007, A.I.Aptekarev and his collaborators discovered a sequence of rational approximations to Euler's constant $\\gamma$ defined by a  linear recurrence. In this paper, we generalize this result and present an  explicit construction of rational approximations for the numbers $\\ln(b)-\\psi(a+1),$ $a, b\\in {\\mathbb Q},$ $b>0, a>-1,$ where $\\psi$ defines the logarithmic derivative of the Euler gamma function. We prove exact formulas for denominators and numerators of the approximations in terms of hypergeometric sums. As a consequence, we get rational approximations for the numbers $\\pi/2\\pm\\gam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0578","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"}