{"id":"W4243705513","doi":"10.1117/3.2207310.ch07","title":"Hermite Polynomials","year":2016,"lang":"en","type":"book-chapter","venue":"","topic":"Mathematics and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Hermite polynomials; Orthogonal polynomials; Harmonic oscillator; Mathematics; Pure mathematics; Cubic Hermite spline; Hermite interpolation; Classical orthogonal polynomials; Hermite spline; Wilson polynomials; Eigenvalues and eigenvectors; Quantum harmonic oscillator; Mathematical analysis; Algebra over a field; Physics; Quantum mechanics; Polynomial","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":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0001303927,0.0002341015,0.0003602791,0.0000600337,0.00004912529,0.00002413183,0.0002138894,0.0002281493,0.01340772],"category_scores_gemma":[0.00003244315,0.0001549493,0.000166244,0.000006850541,0.00004294751,0.00001951974,0.00007688587,0.0001015481,0.00297258],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003010996,"about_ca_system_score_gemma":0.00003408709,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":4.877464e-7,"about_ca_topic_score_gemma":0.000004280045,"domain_scores_codex":[0.9990833,0.000003134414,0.0003759585,0.0002205693,0.0001745378,0.0001424853],"domain_scores_gemma":[0.9986319,0.0003232345,0.000235109,0.0006803697,0.00005440392,0.00007501493],"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":[4.380358e-7,0.000007460145,4.326325e-8,0.00004505872,0.00002822233,8.355542e-7,0.000009150225,1.17201e-9,0.00003433221,0.7628292,0.2351322,0.001913084],"study_design_scores_gemma":[0.00004679521,0.000003681327,4.578038e-8,0.00008702515,0.00002765877,0.000003068219,7.269463e-7,0.00000109581,0.00006532923,0.5239121,0.4757232,0.0001292804],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.000002873877,0.00004105989,0.003643756,0.0005229846,0.00005248666,0.0003323942,0.00005975734,0.0001406829,0.995204],"genre_scores_gemma":[0.00006731432,0.00005392466,0.01345578,0.0001142424,0.000292294,0.00002804259,0.000003745191,0.00008601989,0.9858986],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.240591,"threshold_uncertainty_score":0.9978037,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08575320550571179,"score_gpt":0.3206779797461743,"score_spread":0.2349247742404625,"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."}}