{"paper":{"title":"Ramanujan's cubic transformation and generalized modular equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CA","authors_text":"Miaokun Wang, Yueping Jiang, Yuming Chu","submitted_at":"2013-05-28T15:13:34Z","abstract_excerpt":"We study the quotient of hypergeometric functions \\begin{equation*} \\mu_{a}^*(r)=\\frac{\\pi}{2\\sin{(\\pi a)}}\\frac{F(a,1-a;1;1-r^3)}{F(a,1-a;1;r^3)} \\quad (r\\in(0,1)) \\end{equation*} in the theory of Ramanujan's generalized modular equation for $a\\in(0,1/2]$, find an infinite product formula for $\\mu_{1/3}^*(r)$ by use of the properties of $\\mu_{a}^*(r)$ and Ramanujan's cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan's cubic transformation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6525","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"}