{"paper":{"title":"Zeros of large degree Vorob'ev-Yablonski polynomials via a Hankel determinant identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"nlin.SI","authors_text":"Marco Bertola, Thomas Bothner","submitted_at":"2014-01-06T05:56:43Z","abstract_excerpt":"In the present paper we derive a new Hankel determinant representation for the square of the Vorob'ev-Yablonski polynomial $\\mathcal{Q}_n(x),x\\in\\mathbb{C}$. These polynomials are the major ingredients in the construction of rational solutions to the second Painlev\\'e equation $u_{xx}=xu+2u^3+\\alpha$. As an application of the new identity, we study the zero distribution of $\\mathcal{Q}_n(x)$ as $n\\rightarrow\\infty$ by asymptotically analyzing a certain collection of (pseudo) orthogonal polynomials connected to the aforementioned Hankel determinant. Our approach reproduces recently obtained res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1408","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"}