{"paper":{"title":"Irregular conformal blocks and connection formulae for Painlev\\'e V functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"H. Nagoya, J. Roussillon, O. Lisovyy","submitted_at":"2018-06-21T17:44:10Z","abstract_excerpt":"We prove a Fredholm determinant and short-distance series representation of the Painlev\\'e V tau function $\\tau(t)$ associated to generic monodromy data. Using a relation of $\\tau(t)$ to two different types of irregular $c=1$ Virasoro conformal blocks and the confluence from Painlev\\'e VI equation, connection formulas between the parameters of asymptotic expansions at $0$ and $i\\infty$ are conjectured. Explicit evaluations of the connection constants relating the tau function asymptotics as $t\\to 0,+\\infty,i\\infty$ are obtained. We also show that irregular conformal blocks of rank 1, for arbit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08344","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"}