{"paper":{"title":"Alternating Double Euler Sums, Hypergeometric Identities and a Theorem of Zagier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Lee-Peng Teo","submitted_at":"2017-05-03T06:51:05Z","abstract_excerpt":"In this work, we derive relations between generating functions of double stuffle relations and double shuffle relations to express the alternating double Euler sums $\\zeta\\left(\\overline{r}, s\\right)$, $\\zeta\\left(r, \\overline{s}\\right)$ and $\\zeta\\left(\\overline{r}, \\overline{s}\\right)$ with $r+s$ odd in terms of zeta values. We also give a direct proof of a hypergeometric identity which is a limiting case of a basic hypergeometric identity of Andrews. Finally, we gave another proof for the formula of Zagier on the multiple zeta values $\\zeta(2,\\ldots,2,3,2,\\ldots,2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01269","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"}