{"id":"W1987164720","doi":"10.1016/j.cam.2004.10.021","title":"Orthogonality properties of the Hermite and related polynomials","year":2005,"lang":"en","type":"article","venue":"Journal of Computational and Applied Mathematics","topic":"Mathematical functions and polynomials","field":"Mathematics","cited_by":50,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Victoria","funders":"","keywords":"Mathematics; Hermite polynomials; Orthogonality; Orthogonal polynomials; Classical orthogonal polynomials; Hermite spline; Discrete orthogonal polynomials; Hermite interpolation; Wilson polynomials; Cubic Hermite spline; Gegenbauer polynomials; Order (exchange); Pure mathematics; Algebra over a field; Applied mathematics; Mathematical analysis; Polynomial; Geometry; Statistics","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":[0.002952186,0.0007389801,0.0008142239,0.002341307,0.001059778,0.002802583,0.0008333876,0.001004768,0.004972518],"category_scores_gemma":[0.01222287,0.0004956246,0.0007063578,0.001646465,0.003811848,0.003390821,0.001859196,0.002557636,0.0006018265],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008337255,"about_ca_system_score_gemma":0.001116551,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001054564,"about_ca_topic_score_gemma":0.0008102665,"domain_scores_codex":[0.9983393,0.0005320874,0.00006737973,0.0002101838,0.0005645527,0.0002864659],"domain_scores_gemma":[0.9923732,0.003773982,0.001054869,0.0006978225,0.001465766,0.0006343829],"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":[0.00006430241,0.00003291875,0.000446074,0.00002032798,0.000007810378,0.00005578704,0.0001489077,0.001701294,0.002293312,0.9896497,0.0005575946,0.005022009],"study_design_scores_gemma":[0.00003921261,0.00005635496,0.001193659,0.00002023914,0.00001548999,0.0003648963,0.0002029987,0.05623847,0.002442746,0.9363773,0.002983589,0.00006510071],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5841003,0.001511776,0.3507168,0.001608237,0.0003370633,0.0000696084,0.0004137773,0.0001073575,0.06113509],"genre_scores_gemma":[0.9580039,0.001339925,0.02665886,0.0002640848,0.0006177883,0.00007576699,0.0003555999,0.0001237297,0.01256033],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004972518,"threshold_uncertainty_score":0.0166347,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03408220742330465,"score_gpt":0.2626608191943907,"score_spread":0.2285786117710861,"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."}}