{"paper":{"title":"Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"A. Martinez-Finkelshtein, F. Thabet, M. J. Atia, P. Martinez-Gonzalez","submitted_at":"2013-11-02T12:13:48Z","abstract_excerpt":"In this paper we study the asymptotics (as $n\\to \\infty$) of the sequences of Laguerre polynomials with varying complex parameters $\\alpha$ depending on the degree $n$. More precisely, we assume that $\\alpha_n = n A_n, $ and $ \\lim_n A_n=A \\in \\mathbb{C}$. This study has been carried out previously only for $\\alpha_n\\in \\mathbb{R}$, but complex values of $A$ introduce an asymmetry that makes the problem more difficult.\n  The main ingredient of the asymptotic analysis is the right choice of the contour of orthogonality, which requires the analysis of the global structure of trajectories of an a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0372","kind":"arxiv","version":2},"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"}