{"paper":{"title":"A type of multiple integral with loggamma function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Duokui Yan, Geng-zhe Chang, Rongchang Liu","submitted_at":"2014-04-21T08:43:45Z","abstract_excerpt":"In this paper, we study the multiple integral $ \\displaystyle I= \\int_0^1 \\int_0^1 \\dots \\int_0^1 f(x_1+x_2 + \\dots +x_n) \\, dx_1 \\, dx_2 \\, \\dots \\, dx_n$. A general formula of $I$ is presented. As an application, the integral $I$ with $f(x)= \\log \\Gamma(x)$ is evaluated. We show that the values of $I$ share a common formula for all $n \\in \\mathbb{N}$. The subsidiary computational challenges are substantial and interesting in their own right."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5143","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"}