{"id":"W2407067553","doi":"","title":"A kind of identities for generalized q-harmonic numbers and reciprocals of q-binomial coefficients.","year":2015,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Binomial coefficient; Harmonic number; Binomial (polynomial); Negative binomial distribution; Gaussian binomial coefficient; Harmonic; Statistics; Pure mathematics; Discrete mathematics; Poisson distribution; Riemann hypothesis","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":[0.0005272142,0.0001581084,0.0005485789,0.00008984157,0.00003976714,0.00002093691,0.0001958133,0.00008803694,0.0000167706],"category_scores_gemma":[0.00156317,0.0001515275,0.00009938773,0.0001295194,0.000259974,0.0001678372,0.0001216687,0.00006771224,0.000003113014],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005240292,"about_ca_system_score_gemma":0.00007027984,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002460569,"about_ca_topic_score_gemma":0.000005091475,"domain_scores_codex":[0.9986264,0.00005063731,0.0005829437,0.0001897471,0.000326137,0.0002241389],"domain_scores_gemma":[0.9983295,0.0005933659,0.0003450404,0.0002877575,0.0003393891,0.0001049656],"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":[0.00009324178,0.0001995729,0.0001521958,0.0006183011,0.00006379637,0.000001126117,0.001199353,0.000004216727,0.0011198,0.9926738,0.00382668,0.00004789632],"study_design_scores_gemma":[0.002696846,0.0001698932,0.00001808709,0.00009184884,0.0001076762,0.000004521034,0.0005529608,0.0001610714,0.02547608,0.9704312,0.0001470415,0.0001427523],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9952003,0.0002133653,0.001835998,0.00003028938,0.0006401311,0.0005469961,0.00002869182,0.00003978239,0.00146444],"genre_scores_gemma":[0.9841533,0.00001903895,0.01427051,0.00000934636,0.000009461303,0.00005595338,0.000004621415,0.00003699835,0.001440736],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02435627,"threshold_uncertainty_score":0.6179113,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07337266772921572,"score_gpt":0.3423084657564692,"score_spread":0.2689357980272535,"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."}}