{"paper":{"title":"On a family of symmetric hypergeometric functions of several variables and their Euler type integral representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changgui Zhang, Hua Chen, Zhuangchu Luo","submitted_at":"2011-12-21T10:41:02Z","abstract_excerpt":"This paper is devoted to the family $\\{G_n\\}$ of hypergeometric series of any finite number of variables, the coefficients being the square of the multinomial coefficients $(\\ell_1+...+\\ell_n)!/(\\ell_1!...\\ell_n!)$, where $n\\in\\ZZ_{\\ge 1}$. All these series belong to the family of the general Appell-Lauricella's series. It is shown that each function $G_n$ can be expressed by an integral involving the previous one, $G_{n-1}$. Thus this family can be represented by a multidimensional Euler type integral, what suggests some explicit link with the Gelfand-Kapranov-Zelevinsky's theory of $A$-hyper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4981","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"}