{"id":"W2963230569","doi":"10.5802/jtnb.1023","title":"On a duality formula for certain sums of values of poly-Bernoulli polynomials and its application","year":2018,"lang":"en","type":"article","venue":"Journal de Théorie des Nombres de Bordeaux","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":9,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"","keywords":"Mathematics; Duality (order theory); Bernoulli polynomials; Bernoulli's principle; Bernoulli number; Pure mathematics; Difference polynomials; Combinatorics; Orthogonal polynomials; Physics","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":[0.00257674,0.0008054855,0.001296066,0.003512471,0.001872985,0.002412748,0.001188967,0.001283994,0.004882896],"category_scores_gemma":[0.007378391,0.0003991655,0.001497663,0.002029726,0.004487916,0.004532477,0.003203007,0.004064872,0.0009666046],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001327894,"about_ca_system_score_gemma":0.0006263004,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0004999874,"about_ca_topic_score_gemma":0.0003534403,"domain_scores_codex":[0.9990445,0.0002437638,0.00005450036,0.0001578692,0.0003321023,0.0001671137],"domain_scores_gemma":[0.9981366,0.0008603957,0.000202803,0.0001365384,0.0003720071,0.0002916875],"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":[0.00001496597,0.00001731143,0.0003129106,0.00003423796,0.00000446017,0.000131588,0.00016208,0.0005727453,0.000945499,0.9927408,0.0004883499,0.004575116],"study_design_scores_gemma":[0.000009372229,0.00002381471,0.0002514549,0.0000251809,0.00001099447,0.0002819798,0.00008129346,0.01177708,0.001140815,0.9839965,0.002382858,0.00001873891],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2676789,0.001919316,0.645043,0.002890345,0.001038011,0.0001005882,0.0002018436,0.0002651089,0.08086289],"genre_scores_gemma":[0.8880453,0.001231826,0.09256088,0.001034289,0.001093313,0.0001556236,0.0001904216,0.0002151006,0.01547317],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004882896,"threshold_uncertainty_score":0.01633495,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04135881162851571,"score_gpt":0.3688868947491092,"score_spread":0.3275280831205934,"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."}}