{"paper":{"title":"Complexity analysis of hypergeometric orthogonal polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. Guerrero, J.S. Dehesa, P. S\\'anchez-Moreno","submitted_at":"2014-08-20T15:36:25Z","abstract_excerpt":"The complexity measures of the Cr\\'amer-Rao, Fisher-Shannon and LMC (L\\'opez-Ruiz, Mancini and Calvet) types of the Rakhmanov probability density $\\rho_n(x)=\\omega(x) p_n^2(x)$ of the polynomials $p_n(x)$ orthogonal with respect to the weight function $\\omega(x)$, $x\\in (a,b)$, are used to quantify various two-fold facets of the spreading of the Hermite, Laguerre and Jacobi systems all over their corresponding orthogonality intervals in both analytical and computational ways. Their explicit (Cr\\'amer-Rao) and asymptotical (Fisher-Shannon, LMC) values are given for the three systems of orthogon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4698","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"}