{"id":"W1977239245","doi":"10.1016/j.cam.2004.01.031","title":"A characterization of classical and semiclassical orthogonal polynomials from their dual polynomials","year":2004,"lang":"en","type":"article","venue":"Journal of Computational and Applied Mathematics","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":53,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"","keywords":"Mathematics; Orthogonal polynomials; Semiclassical physics; Classical orthogonal polynomials; Discrete orthogonal polynomials; Characterization (materials science); Dual (grammatical number); Gegenbauer polynomials; Jacobi polynomials; Wilson polynomials; Hahn polynomials; Difference polynomials; Pure mathematics; Algebra over a field; Quantum; Quantum mechanics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001297714,0.0005970007,0.0006479921,0.003071948,0.00145407,0.003526078,0.001027466,0.0009112973,0.003842907],"category_scores_gemma":[0.005135085,0.0003368123,0.0007323896,0.001950006,0.003387828,0.00405254,0.002357124,0.002938956,0.0006936319],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0009875341,"about_ca_system_score_gemma":0.0008139558,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004359534,"about_ca_topic_score_gemma":0.0004040302,"domain_scores_codex":[0.9990158,0.0001819527,0.00004684744,0.0001769392,0.0003577824,0.0002207328],"domain_scores_gemma":[0.9974291,0.0008617556,0.000473768,0.0002453344,0.0005160958,0.0004741244],"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":[0.00005512752,0.00002302605,0.0002462043,0.00001938897,0.000003516124,0.00004740453,0.0001363963,0.0002502114,0.001353218,0.9908847,0.0005160328,0.006464784],"study_design_scores_gemma":[0.00002031648,0.00003389168,0.0005080987,0.00002324519,0.000008338075,0.0002773487,0.0001240241,0.008365359,0.001400845,0.9846684,0.004536921,0.00003321024],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.677917,0.001189405,0.2420546,0.002130714,0.0006912359,0.00007707503,0.0007250725,0.0002404684,0.07497456],"genre_scores_gemma":[0.9544774,0.0006052334,0.03270324,0.0003869421,0.0009494671,0.0000512025,0.0006040864,0.0001242856,0.01009804],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003842907,"threshold_uncertainty_score":0.01285583,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02697967117808685,"score_gpt":0.260310980746718,"score_spread":0.2333313095686312,"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."}}