{"paper":{"title":"Variations on a Hypergeometric Theme","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Michael Milgram","submitted_at":"2018-03-07T01:49:56Z","abstract_excerpt":"The question was asked: Is it possible to express the function \\begin{equation} \\tag{1.1} h(a)\\equiv\\,{_4F_3}(a,a,a,a;2a,a+1,a+1;1) \\label{question} \\end{equation} in closed form? After considerable analysis, the answer appears to be \"no\", but during the attempt to answer this question, a number of interesting (and unexpected) related results were obtained, either as specialized transformations, or as closed-form expressions for several related functions. The purpose of this paper is to record and review both the methods attempted and the related identities obtained (specifically new $_4F_3(1)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.03135","kind":"arxiv","version":3},"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"}