{"paper":{"title":"Multiple Clausen values and deformed Ap\\'ery-like series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO"],"primary_cat":"math.NT","authors_text":"Yajun Zhou, Zhi-Wei Sun","submitted_at":"2026-07-16T07:15:40Z","abstract_excerpt":"With generalized central binomial coefficients $ \\binom{2x}{x}:=\\frac{\\Gamma(2x+1)}{[\\Gamma(x+1)]^2}$ defined through Euler's gamma function, we represent deformed Ap\\'ery-like series \\[ \\mathscr A_{s,n}:=\\sum_{k=1}^\\infty\\left.\\!\\frac{\\partial^n}{\\partial x^n}\\frac{1}{x^s\\binom{2x}{x}}\\right|_{x=k} \\] by multiple Clausen values (MCVs), which belong to a special class of cyclotomic multiple zeta values (CMZVs) at level $3$. For example, exploiting provable algebraic relations among MCVs, we show that \\[\\mathscr A_{1,5}=-\\frac{9[495L(\\chi_{-3},6)-30\\pi^{2}L(\\chi_{-3},4)-2\\pi^{4}L(\\chi_{-3},2)]}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14646","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/2607.14646/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"}