{"paper":{"title":"Approximations for Apery's constant $\\zeta(3)$ and rational series representations involving $\\zeta(2n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NT"],"primary_cat":"math.CA","authors_text":"Cezar Lupu, Derek Orr","submitted_at":"2016-05-31T09:22:45Z","abstract_excerpt":"In this note, using an idea from \\cite{Amo-Carrillo-Sanchez} we derive some new series representations involving $\\zeta(2n)$ and Euler numbers. Using a well-known series representation for the Clausen function, we also provide some new representations of Apery's constant $\\zeta(3)$. In particular cases, we recover some well-known series representations of $\\pi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09541","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"}