{"paper":{"title":"Asymptotics of type I Hermite-Pad\\'e polynomials for semiclassical functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Andrei Mart\\'inez-Finkelshtein, Evgenii A. Rakhmanov, Sergeiy P. Suetin","submitted_at":"2015-02-04T14:16:39Z","abstract_excerpt":"Type I Hermite--Pad\\'e polynomials for a set of functions $f_0, f_1, ..., f_s$ at infinity, $Q_{n,0}$, $Q_{n,1}$, ..., $Q_{n,s}$, is defined by the asymptotic condition $$ R_n(z):=\\bigl(Q_{n,0}f_0+Q_{n,1}f_1+Q_{n,2}f_2+...+Q_{n,s}f_s\\bigr)(z) =\\mathcal O (\\frac1{z^{s n+s}}), \\quad z\\to\\infty, $$ with the degree of all $Q_{n,k}\\leq n$. We describe an approach for finding the asymptotic zero distribution of these polynomials as $n\\to \\infty$ under the assumption that all $f_j$'s are semiclassical, i.e. their logarithmic derivatives are rational functions. In this situation $R_n$ and $Q_{n,k}f_k$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01202","kind":"arxiv","version":3},"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"}