{"id":"W2058914001","doi":"10.1016/j.jmaa.2011.09.014","title":"Two-step Darboux transformations and exceptional Laguerre polynomials","year":2011,"lang":"en","type":"article","venue":"Journal of Mathematical Analysis and Applications","topic":"Quantum Mechanics and Non-Hermitian Physics","field":"Physics and Astronomy","cited_by":132,"is_retracted":false,"has_abstract":false,"ca_institutions":"Dalhousie University; McGill University","funders":"","keywords":"Laguerre polynomials; Mathematics; Orthogonal polynomials; Classical orthogonal polynomials; Hermite polynomials; Discrete orthogonal polynomials; Wilson polynomials; Transformation (genetics); Pure mathematics; Jacobi polynomials; Laguerre's method; Algebra over a field","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002582042,0.0001060537,0.0003215555,0.0001292156,0.0001333841,0.00004452709,0.00009923484,0.00002413473,0.0006795024],"category_scores_gemma":[0.000002646981,0.00008166119,0.0002094885,0.0002884444,0.00005981498,0.0001491075,0.00002062095,0.0001190007,0.00001454086],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000005370131,"about_ca_system_score_gemma":0.00002454184,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009354106,"about_ca_topic_score_gemma":0.000002016598,"domain_scores_codex":[0.9991321,0.00002459196,0.00047953,0.0001029216,0.0001483082,0.000112564],"domain_scores_gemma":[0.9992935,0.00007620779,0.0002521307,0.0001252701,0.0001058427,0.0001470441],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000005549065,0.0002758234,0.00115455,0.00001573296,0.0005738616,3.296115e-7,0.0002998716,0.000004185821,0.0004746915,0.9842771,0.0000597924,0.01285857],"study_design_scores_gemma":[0.0005695954,0.00005971669,0.003827726,0.00002773662,0.001746169,0.0000154421,0.0008539452,0.006078161,0.0009192234,0.984682,0.001003231,0.0002170115],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1377182,0.00008659305,0.8471336,0.0001962339,0.00001048694,0.0001386865,0.00005431246,0.000006232422,0.0146556],"genre_scores_gemma":[0.9923708,0.00002427957,0.007318621,0.00002691726,0.0001673833,0.00002205098,0.000008781981,0.000007095614,0.0000540513],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8546526,"threshold_uncertainty_score":0.7440075,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01821949546052774,"score_gpt":0.262874820166458,"score_spread":0.2446553247059302,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}