{"paper":{"title":"An Asymptotic Series for an Integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.PR"],"primary_cat":"math.NT","authors_text":"Guy Louchard, Markus Kuba, Michael E. Hoffman, Moti Levy","submitted_at":"2018-02-26T09:28:49Z","abstract_excerpt":"We obtain an asymptotic series $\\sum_{j=0}^\\infty\\frac{I_j}{n^j}$ for the integral $\\int_0^1[x^n+(1-x)^n]^{\\frac1{n}}dx$ as $n\\to\\infty$, and compute $I_j$ in terms of alternating (or \"colored\") multiple zeta value. We also show that $I_j$ is a rational polynomial the ordinary zeta values, and give explicit formulas for $j\\le 12$. As a byproduct, we obtain precise results about the convergence of norms of random variables and their moments. We study $\\Vert(U,1-U)\\Vert_n$ as $n$ tends to infinity and we also discuss $\\Vert(U_1,U_2,\\dots,U_r)\\Vert_n$ for standard uniformly distributed random var"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09214","kind":"arxiv","version":2},"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"}