{"paper":{"title":"The complex WKB method for difference equations and Airy functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Alexander Fedotov, Fr\\'ed\\'eric Klopp (IMJ-PRG)","submitted_at":"2018-10-11T09:19:29Z","abstract_excerpt":"We consider the difference Schr{\\\"o}dinger equation $\\psi$(z + h) + $\\psi$(z -- h) + v(z)$\\psi$(z) = 0 where z is a complex variable, h > 0 is a parameter, and v is an analytic function. As h $\\rightarrow$ 0 analytic solutions to this equation have a standard quasiclassical behavior near the points where v(z) = $\\pm$2. We study analytic solutions near the points z 0 satisfying v(z 0) = $\\pm$2 and v (z 0) = 0. For the finite difference equation, these points are the natural analogues of the simple turning points defined for the differential equation --$\\psi$ (z) + v(z)$\\psi$(z) = 0. In an h-ind"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04918","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"}