{"id":"W2576212255","doi":"","title":"Some Recurrence Relations For q-Bernoulli Numbers And Polynomials.","year":2016,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Recurrence relation; Bernoulli's principle; Bernoulli number; Bernoulli polynomials; Pure mathematics; Combinatorics; Algebra over a field; Discrete mathematics; Orthogonal polynomials; Difference polynomials; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000238715,0.0001398078,0.0002338989,0.00004916023,0.0001359389,0.00003182153,0.000139291,0.00008079716,0.0000492207],"category_scores_gemma":[0.001938167,0.0001055564,0.0000601694,0.00006773279,0.000150011,0.000418535,0.0000739606,0.00006495078,0.00007002166],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006987465,"about_ca_system_score_gemma":0.00002918471,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004175583,"about_ca_topic_score_gemma":0.000004831467,"domain_scores_codex":[0.9990605,0.00002879586,0.0002882094,0.0002256551,0.0001464569,0.0002503466],"domain_scores_gemma":[0.9973738,0.002032222,0.0001268147,0.0002921024,0.00007960705,0.00009551605],"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":[0.000008215507,0.00005064758,0.0002172682,0.00005768934,0.00001809924,7.161437e-7,0.0001635308,3.756151e-8,0.0003291732,0.9887401,0.01002801,0.0003864658],"study_design_scores_gemma":[0.0008058405,0.00004606707,0.00009759058,0.0001313604,0.00003298539,0.00000406087,0.00005754187,0.000009769223,0.001205681,0.9955946,0.001849307,0.0001651675],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9746875,0.0007506309,0.008363527,0.003591373,0.003035437,0.001483346,0.00009574804,0.0004539893,0.007538483],"genre_scores_gemma":[0.9542148,0.0001465039,0.02530971,0.00005095049,0.00005102244,0.0002002191,0.000002797757,0.00006763557,0.01995641],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02047271,"threshold_uncertainty_score":0.4304465,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03452984200485717,"score_gpt":0.3131882864558034,"score_spread":0.2786584444509462,"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."}}