{"id":"W2406622082","doi":"","title":"Identities For The Bernoulli And Euler Numbers And Polynomials.","year":2012,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"History and Theory of Mathematics","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Bernoulli's principle; Euler's formula; Bernoulli polynomials; Pure mathematics; Algebra over a field; Difference polynomials; Orthogonal polynomials; Mathematical analysis; Physics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001387138,0.0005468639,0.0006221958,0.002585155,0.002465152,0.003606583,0.0007833201,0.001282509,0.01154645],"category_scores_gemma":[0.004805861,0.0003737311,0.0006152305,0.002043747,0.005225306,0.008652371,0.002118548,0.003716885,0.00329222],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002581277,"about_ca_system_score_gemma":0.001246142,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002217403,"about_ca_topic_score_gemma":0.002636972,"domain_scores_codex":[0.9990768,0.0003197191,0.00004776044,0.0001349361,0.0003237465,0.00009696625],"domain_scores_gemma":[0.9985569,0.0007048172,0.0001289869,0.0001845361,0.0003048354,0.0001198291],"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":[0.000001498487,0.000001609391,0.00002454532,0.000008665687,6.552227e-7,0.000007180991,0.00004408511,0.00003030154,0.00002517489,0.996626,0.00178301,0.001447291],"study_design_scores_gemma":[0.000001827229,0.000001848872,0.00007670933,0.00001456899,0.000001186883,0.00004310059,0.00002805473,0.0001666299,0.0000433461,0.9829059,0.01671384,0.000003004374],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.02599935,0.04945517,0.110206,0.01421514,0.004139274,0.00003335978,0.0008636697,0.0002150228,0.7948731],"genre_scores_gemma":[0.7281395,0.027365,0.04512776,0.003331394,0.005429167,0.0001377557,0.0008760322,0.0001985324,0.1893948],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01154645,"threshold_uncertainty_score":0.03862679,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03365641134269772,"score_gpt":0.2852986123350206,"score_spread":0.2516422009923229,"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."}}