{"id":"W1986615719","doi":"10.1016/j.amc.2013.10.056","title":"Polynomial solutions for a class of second-order linear differential equations","year":2013,"lang":"en","type":"article","venue":"Applied Mathematics and Computation","topic":"Quantum Mechanics and Non-Hermitian Physics","field":"Physics and Astronomy","cited_by":10,"is_retracted":false,"has_abstract":false,"ca_institutions":"Concordia University; University of Prince Edward Island","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Polynomial; Orthogonality; Differential equation; Linear differential equation; Class (philosophy); Matrix polynomial; Reciprocal polynomial; Degree (music); Differential (mechanical device); Order (exchange); Applied mathematics; Mathematical analysis; Pure mathematics; Physics; Computer science; Geometry","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0005922989,0.0007737476,0.0009603433,0.001166009,0.0009474827,0.00215832,0.001164307,0.00183911,0.005402819],"category_scores_gemma":[0.003407295,0.000383977,0.0007929776,0.001036814,0.001652351,0.00219763,0.001345959,0.002369371,0.0005862301],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001297702,"about_ca_system_score_gemma":0.001159184,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001834455,"about_ca_topic_score_gemma":0.001475966,"domain_scores_codex":[0.9996326,0.00007729895,0.00001551892,0.00005188592,0.0001330064,0.00008971104],"domain_scores_gemma":[0.999146,0.000405443,0.0001314835,0.00004703383,0.0001481156,0.0001218379],"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":[0.00002544642,0.00003405114,0.0001898524,0.00006366416,0.00001143955,0.0001554507,0.0001873363,0.007751605,0.00150736,0.9841099,0.001405494,0.004558467],"study_design_scores_gemma":[0.0000623451,0.0000312157,0.00033294,0.00001663143,0.000008970133,0.0002973606,0.0001284259,0.1572222,0.0005280405,0.8382886,0.003054076,0.00002919079],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3439254,0.002606685,0.5764039,0.005913307,0.0006502458,0.0001674613,0.0005995957,0.0003622761,0.0693711],"genre_scores_gemma":[0.9159168,0.001582466,0.03385354,0.0004156709,0.0006225005,0.00009778245,0.0003527678,0.0001073515,0.04705126],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005402819,"threshold_uncertainty_score":0.01807427,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02070796780765535,"score_gpt":0.2525709582192721,"score_spread":0.2318629904116167,"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."}}