{"paper":{"title":"Olver's asymptotic method: a special case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Chelo Ferreira, Ester Perez Sinusia, Jose L. Lopez","submitted_at":"2014-06-06T09:07:05Z","abstract_excerpt":"We consider the asymptotic method designed by F. Olver [Olver, 1974] for linear differential equations of the second order containing a large (asymptotic) parameter $\\Lambda$: $x^my\"-\\Lambda^2y=g(x)y$, with $m\\in\\mathbb{Z}$ and $g$ continuous. Olver studies in detail the cases $m\\ne 2$, specially the cases $m=0,\\pm 1$, giving the Poincar\\'e-type asymptotic expansion of two independent solutions of the equation. The case $m=2$ is different, as the behavior of the solutions for large $\\Lambda$ is not of exponential type, but of power type. In this case, Olver's theory does not give as many detai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.1613","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"}