{"paper":{"title":"Connection Formulae for Asymptotics of the Fifth Painlev\\'e Transcendent on the Imaginary Axis: I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"A. V. Kitaev, F. V. Andreev","submitted_at":"2019-04-14T19:04:05Z","abstract_excerpt":"Leading terms of asymptotic expansions for the general complex solutions of the fifth Painlev\\'e equation as $t\\to\\imath\\infty$ are found. These asymptotics are parameterized by monodromy data of the associated linear ODE. $$ \\frac{d}{d\\lambda}Y= \\left(\\frac t2\\sigma_3 + \\frac{A_0}\\lambda+\\frac{A_1}{\\lambda-1}\\right)Y. $$ The parametrization allows one to derive connection formulas for the asymptotics. We provide numerical verification of the results. Important special cases of the connection formulas are also considered."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06741","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"}