{"paper":{"title":"Accelerating the Hypergeometric Function with the Beta Integral to Derive New Infinite Series for $\\pi$ and Values of the Gamma Function","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Cetin Hakimoglu","submitted_at":"2024-02-12T19:40:33Z","abstract_excerpt":"The beta integral is applied to accelerate the hypergeometric function $2 F 1\\left\\{1, B; C ; w\\right\\}$ to derive new infinite series for constants such as $\\pi$ and values of the gamma function. A compendium of new infinite series is given. Ramanujan-like formulas for pi are also derived based on elementary inverse trigonometric functions, including a formula with rational values that adds 2.5 digits per terms, which makes the series much more compact than similar formulas in the existing literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.08693","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2402.08693/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}