{"id":"W2069226673","doi":"10.1006/jath.2000.3550","title":"A Unified Calculus Using the Generalized Bernoulli Polynomials","year":2001,"lang":"en","type":"article","venue":"Journal of Approximation Theory","topic":"Mathematical and Theoretical Analysis","field":"Mathematics","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"Polytechnique Montréal","funders":"","keywords":"Mathematics; Bernoulli's principle; Remainder; Calculus (dental); Time-scale calculus; Differential calculus; Context (archaeology); Algebra over a field; Bessel function; Function (biology); Point (geometry); Pure mathematics; Mathematical analysis; Multivariable calculus; Arithmetic","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":[0.002668526,0.0009680326,0.002015488,0.002884564,0.002044982,0.004007386,0.002027632,0.001743231,0.003200424],"category_scores_gemma":[0.003734297,0.0007239594,0.002353028,0.00241826,0.004414097,0.007641031,0.003684611,0.003729002,0.000766204],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001709182,"about_ca_system_score_gemma":0.001554676,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001403465,"about_ca_topic_score_gemma":0.001467508,"domain_scores_codex":[0.9985574,0.0005059645,0.00008127423,0.0002150155,0.0004870744,0.0001532474],"domain_scores_gemma":[0.9989718,0.0002940406,0.000108455,0.0002207732,0.0002241664,0.000180784],"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":[0.000003109655,0.000003357174,0.00001882296,0.000007146353,0.000003246554,0.00001876502,0.00002855923,0.00056075,0.0001622753,0.9976864,0.0002254627,0.00128213],"study_design_scores_gemma":[0.000004836308,0.000007940684,0.00003762473,0.000007244044,0.000005690564,0.00004514671,0.00001374823,0.01125214,0.00008562487,0.9862322,0.002296712,0.00001101635],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04201223,0.003194462,0.9066861,0.002426967,0.001865249,0.0000662127,0.000144019,0.0001674636,0.04343735],"genre_scores_gemma":[0.5397702,0.005116534,0.4096485,0.001477398,0.004113127,0.0002079038,0.0001981879,0.0002960986,0.03917211],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004007386,"threshold_uncertainty_score":0.01411271,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05931920575158067,"score_gpt":0.3273809673729354,"score_spread":0.2680617616213547,"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."}}