{"paper":{"title":"Power expansions for solution of the fourth-order analog to the first Painlev\\'{e} equation","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Nikolai A. Kudryashov, Olga Yu. Efimova","submitted_at":"2005-07-14T11:56:18Z","abstract_excerpt":"One of the fourth-order analog to the first Painlev\\'{e} equation is studied. All power expansions for solutions of this equation near points $z=0$ and $z=\\infty$ are found by means of the power geometry method. The exponential additions to the expansion of solution near $z=\\infty$ are computed. The obtained results confirm the hypothesis that the fourth-order analog of the first Painlev\\'{e} equation determines new transcendental functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0507026","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"}