{"paper":{"title":"Construction and implementation of asymptotic expansions for Laguerre-type orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"cs.NA","authors_text":"Daan Huybrechs, Peter Opsomer","submitted_at":"2016-12-22T12:36:19Z","abstract_excerpt":"Laguerre and Laguerre-type polynomials are orthogonal polynomials on the interval $[0,\\infty)$ with respect to a weight function of the form $w(x) = x^{\\alpha} e^{-Q(x)}, Q(x) = \\sum_{k=0}^m q_k x^k, \\alpha > -1, q_m > 0$. The classical Laguerre polynomials correspond to $Q(x)=x$. The computation of higher-order terms of the asymptotic expansions of these polynomials for large degree becomes quite complicated, and a full description seems to be lacking in literature. However, this information is implicitly available in the work of Vanlessen, based on a non-linear steepest descent analysis of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07578","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"}