{"id":"W1973670074","doi":"10.1016/j.cam.2009.07.038","title":"New formulae for higher order derivatives and applications","year":2009,"lang":"en","type":"article","venue":"Journal of Computational and Applied Mathematics","topic":"Nonlinear Waves and Solitons","field":"Physics and Astronomy","cited_by":17,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Bessel function; Hermite polynomials; Legendre function; Extrapolation; Legendre polynomials; Applied mathematics; Bessel polynomials; Order (exchange); Second derivative; Differential equation; Chebyshev filter; Mathematical analysis; Orthogonal polynomials; Classical orthogonal polynomials; Gegenbauer polynomials","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":[0.00005404111,0.00006693504,0.000140337,0.0000278032,0.00007008271,0.00003654894,0.00003855931,0.00001429622,0.00001958606],"category_scores_gemma":[0.000001290748,0.00005143127,0.00003144241,0.00004573735,0.00001686796,0.00004795294,0.000008285383,0.00004900232,6.11436e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00000278942,"about_ca_system_score_gemma":0.00003727964,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":2.214715e-7,"about_ca_topic_score_gemma":2.321608e-8,"domain_scores_codex":[0.9995897,0.000001581955,0.0002149089,0.00005003916,0.00007767899,0.00006607139],"domain_scores_gemma":[0.9995413,0.0001192712,0.0001609372,0.00002934273,0.00008336869,0.00006580917],"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":[0.000007560806,0.00007817498,0.00002234031,0.00001630015,0.00003438916,4.985531e-8,0.0002029411,0.0007052596,0.0001548419,0.9571169,0.0004432829,0.04121798],"study_design_scores_gemma":[0.0005804905,0.00004776043,0.0008105544,0.00001259263,0.00002829429,0.00000421091,0.0001595744,0.002441053,0.0001167863,0.9873674,0.008362827,0.00006849476],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"methods","genre_scores_codex":[0.02022335,0.00005264119,0.9763011,0.0005677658,0.00001355809,0.0001566307,0.0000095594,0.000003518102,0.002671869],"genre_scores_gemma":[0.372732,0.000002474711,0.6264272,0.00009587817,0.0004873544,0.000003417626,0.000007502454,0.0000056244,0.0002385238],"genre_candidate":"methods","genre_consensus":"methods","teacher_disagreement_score":0.3525086,"threshold_uncertainty_score":0.2097306,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01274693776418943,"score_gpt":0.2763891710808737,"score_spread":0.2636422333166843,"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."}}